diff --git a/packages/circom/tests/caret.test.js b/packages/circom/tests/caret.test.js
index 909732d..d4ffdfd 100644
--- a/packages/circom/tests/caret.test.js
+++ b/packages/circom/tests/caret.test.js
@@ -104,7 +104,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret1.json"),
+                path.join(__dirname, "./circuits/caret1.json"),
                 "utf8"
             )
         )[0];
@@ -129,7 +129,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret1.json"),
+                path.join(__dirname, "./circuits/caret1.json"),
                 "utf8"
             )
         )[0];
@@ -150,7 +150,7 @@ describe("Caret Regex", () => {
         };
         const witness = await circuit1.calculateWitness(circuitInputs);
         await circuit1.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
@@ -164,7 +164,7 @@ describe("Caret Regex", () => {
         };
         const witness = await circuit1.calculateWitness(circuitInputs);
         await circuit1.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
@@ -183,7 +183,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret2.json"),
+                path.join(__dirname, "./circuits/caret2.json"),
                 "utf8"
             )
         )[0];
@@ -208,7 +208,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret2.json"),
+                path.join(__dirname, "./circuits/caret2.json"),
                 "utf8"
             )
         )[0];
@@ -233,7 +233,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret2.json"),
+                path.join(__dirname, "./circuits/caret2.json"),
                 "utf8"
             )
         )[0];
@@ -254,14 +254,14 @@ describe("Caret Regex", () => {
         };
         const witness = await circuit2.calculateWitness(circuitInputs);
         await circuit2.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
     it("caret3 valid case 1", async () => {
-        const inputStr = `a7hv8a9b`;
+        const inputStr = `bb817267`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -272,7 +272,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret3.json"),
+                path.join(__dirname, "./circuits/caret3.json"),
                 "utf8"
             )
         )[0];
@@ -285,8 +285,8 @@ describe("Caret Regex", () => {
         }
     });
 
-    it("caret3 invalid case 1", async () => {
-        const inputStr = ``;
+    it("caret3 valid case 2", async () => {
+        const inputStr = `818abbb9`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -297,7 +297,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret3.json"),
+                path.join(__dirname, "./circuits/caret3.json"),
                 "utf8"
             )
         )[0];
@@ -310,8 +310,22 @@ describe("Caret Regex", () => {
         }
     });
 
+    it("caret3 invalid case 1", async () => {
+        const inputStr = `81b`;
+        const paddedStr = apis.padString(inputStr, 8);
+        const circuitInputs = {
+            msg: paddedStr,
+        };
+        const witness = await circuit3.calculateWitness(circuitInputs);
+        await circuit3.checkConstraints(witness);
+        expect(0n).toEqual(witness[1]);
+        for (let idx = 0; idx < 8; ++idx) {
+            expect(0n).toEqual(witness[2 + idx]);
+        }
+    });
+
     it("caret4 valid case 1", async () => {
-        const inputStr = `abaaabba`;
+        const inputStr = `xabaaabb`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -322,7 +336,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret4.json"),
+                path.join(__dirname, "./circuits/caret4.json"),
                 "utf8"
             )
         )[0];
@@ -336,7 +350,7 @@ describe("Caret Regex", () => {
     });
 
     it("caret4 valid case 2", async () => {
-        const inputStr = `baab82ab`;
+        const inputStr = `xbaab82a`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -347,7 +361,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret4.json"),
+                path.join(__dirname, "./circuits/caret4.json"),
                 "utf8"
             )
         )[0];
@@ -361,7 +375,7 @@ describe("Caret Regex", () => {
     });
 
     it("caret4 valid case 3", async () => {
-        const inputStr = `7w1\nabba`;
+        const inputStr = `7w1\nxabb`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -372,7 +386,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret4.json"),
+                path.join(__dirname, "./circuits/caret4.json"),
                 "utf8"
             )
         )[0];
@@ -386,7 +400,7 @@ describe("Caret Regex", () => {
     });
 
     it("caret4 valid case 4", async () => {
-        const inputStr = `7w\nbbba9`;
+        const inputStr = `7w\nxbbb9`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -397,7 +411,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret4.json"),
+                path.join(__dirname, "./circuits/caret4.json"),
                 "utf8"
             )
         )[0];
@@ -412,35 +426,35 @@ describe("Caret Regex", () => {
 
 
     it("caret4 invalid case 1", async () => {
-        const inputStr = `7w1nabba`;
+        const inputStr = `7w1nxaba`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit4.calculateWitness(circuitInputs);
         await circuit4.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
     it("caret4 invalid case 2", async () => {
-        const inputStr = `7wnbbba9`;
+        const inputStr = `abba\nx`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit4.calculateWitness(circuitInputs);
         await circuit4.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
     it("caret5 valid case 1", async () => {
-        const inputStr = `defabc81`;
+        const inputStr = `xdefabc1`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -451,7 +465,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret5.json"),
+                path.join(__dirname, "./circuits/caret5.json"),
                 "utf8"
             )
         )[0];
@@ -465,7 +479,7 @@ describe("Caret Regex", () => {
     });
 
     it("caret5 valid case 2", async () => {
-        const inputStr = `91\n9eabc`;
+        const inputStr = `9\nx9eabc`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
@@ -476,7 +490,7 @@ describe("Caret Regex", () => {
         const prefixIdxes = apis.extractSubstrIdxes(
             inputStr,
             readFileSync(
-                path.join(__dirname, "../circuits/common/caret5.json"),
+                path.join(__dirname, "./circuits/caret5.json"),
                 "utf8"
             )
         )[0];
@@ -490,60 +504,61 @@ describe("Caret Regex", () => {
     });
 
     it("caret5 invalid case 1", async () => {
-        const inputStr = `abc`;
+        const inputStr = `xabc`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit5.calculateWitness(circuitInputs);
         await circuit5.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
-
     it("caret5 invalid case 2", async () => {
-        const inputStr = `a8abc8`;
+        const inputStr = `1\ndef`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit5.calculateWitness(circuitInputs);
         await circuit5.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
-    it("caret5 invalid case 2", async () => {
-        const inputStr = `71\na81ma`;
+
+
+    it("caret5 invalid case 3", async () => {
+        const inputStr = `a8abc8`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit5.calculateWitness(circuitInputs);
         await circuit5.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
 
-
-    it("caret5 invalid case 3", async () => {
-        const inputStr = `91n9eabc`;
+    it("caret5 invalid case 4", async () => {
+        const inputStr = `71\na81ma`;
         const paddedStr = apis.padString(inputStr, 8);
         const circuitInputs = {
             msg: paddedStr,
         };
         const witness = await circuit5.calculateWitness(circuitInputs);
         await circuit5.checkConstraints(witness);
-        expect(1n).toEqual(witness[1]);
+        expect(0n).toEqual(witness[1]);
         for (let idx = 0; idx < 8; ++idx) {
             expect(0n).toEqual(witness[2 + idx]);
         }
     });
+
 });
diff --git a/packages/circom/tests/circuits/caret1_regex.circom b/packages/circom/tests/circuits/caret1_regex.circom
index 40521ea..4fd42a8 100644
--- a/packages/circom/tests/circuits/caret1_regex.circom
+++ b/packages/circom/tests/circuits/caret1_regex.circom
@@ -14,52 +14,60 @@ template Caret1Regex(msg_bytes) {
 		in[i+1] <== msg[i];
 	}
 
-	component eq[1][num_bytes];
-	component and[1][num_bytes];
-	signal states[num_bytes+1][2];
-	signal states_tmp[num_bytes+1][2];
+	component eq[2][num_bytes];
+	component and[2][num_bytes];
+	signal states[num_bytes+1][3];
+	signal states_tmp[num_bytes+1][3];
 	signal from_zero_enabled[num_bytes+1];
 	from_zero_enabled[num_bytes] <== 0;
 	component state_changed[num_bytes];
 
-	for (var i = 1; i < 2; i++) {
+	for (var i = 1; i < 3; i++) {
 		states[0][i] <== 0;
 	}
 
 	for (var i = 0; i < num_bytes; i++) {
-		state_changed[i] = MultiOR(1);
+		state_changed[i] = MultiOR(2);
 		states[i][0] <== 1;
 		eq[0][i] = IsEqual();
 		eq[0][i].in[0] <== in[i];
-		eq[0][i].in[1] <== 97;
+		eq[0][i].in[1] <== 255;
 		and[0][i] = AND();
 		and[0][i].a <== states[i][0];
 		and[0][i].b <== eq[0][i].out;
 		states_tmp[i+1][1] <== 0;
-		from_zero_enabled[i] <== MultiNOR(1)([states_tmp[i+1][1]]);
+		eq[1][i] = IsEqual();
+		eq[1][i].in[0] <== in[i];
+		eq[1][i].in[1] <== 97;
+		and[1][i] = AND();
+		and[1][i].a <== states[i][1];
+		and[1][i].b <== eq[1][i].out;
+		states[i+1][2] <== and[1][i].out;
+		from_zero_enabled[i] <== MultiNOR(2)([states_tmp[i+1][1], states[i+1][2]]);
 		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[0][i].out]);
 		state_changed[i].in[0] <== states[i+1][1];
+		state_changed[i].in[1] <== states[i+1][2];
 	}
 
 	component final_state_result = MultiOR(num_bytes+1);
 	for (var i = 0; i <= num_bytes; i++) {
-		final_state_result.in[i] <== states[i][1];
+		final_state_result.in[i] <== states[i][2];
 	}
 	out <== final_state_result.out;
 	signal is_consecutive[msg_bytes+1][3];
 	is_consecutive[msg_bytes][2] <== 0;
 	for (var i = 0; i < msg_bytes; i++) {
-		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][1] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
+		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][2] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
 		is_consecutive[msg_bytes-1-i][1] <== state_changed[msg_bytes-i].out * is_consecutive[msg_bytes-1-i][0];
-		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][1], is_consecutive[msg_bytes-1-i][1]]);
+		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][2], is_consecutive[msg_bytes-1-i][1]]);
 	}
-	// substrings calculated: [{(0, 1)}]
+	// substrings calculated: [{(1, 2)}]
 	signal is_substr0[msg_bytes];
 	signal is_reveal0[msg_bytes];
 	signal output reveal0[msg_bytes];
 	for (var i = 0; i < msg_bytes; i++) {
-		 // the 0-th substring transitions: [(0, 1)]
-		is_substr0[i] <== MultiOR(1)([states[i+1][0] * states[i+2][1]]);
+		 // the 0-th substring transitions: [(1, 2)]
+		is_substr0[i] <== MultiOR(1)([states[i+1][1] * states[i+2][2]]);
 		is_reveal0[i] <== is_substr0[i] * is_consecutive[i][2];
 		reveal0[i] <== in[i+1] * is_reveal0[i];
 	}
diff --git a/packages/circom/tests/circuits/caret2_regex.circom b/packages/circom/tests/circuits/caret2_regex.circom
index 0f3ff7e..725b0cc 100644
--- a/packages/circom/tests/circuits/caret2_regex.circom
+++ b/packages/circom/tests/circuits/caret2_regex.circom
@@ -14,63 +14,71 @@ template Caret2Regex(msg_bytes) {
 		in[i+1] <== msg[i];
 	}
 
-	component eq[3][num_bytes];
-	component and[1][num_bytes];
+	component eq[4][num_bytes];
+	component and[2][num_bytes];
 	component multi_or[1][num_bytes];
-	signal states[num_bytes+1][2];
-	signal states_tmp[num_bytes+1][2];
+	signal states[num_bytes+1][3];
+	signal states_tmp[num_bytes+1][3];
 	signal from_zero_enabled[num_bytes+1];
 	from_zero_enabled[num_bytes] <== 0;
 	component state_changed[num_bytes];
 
-	for (var i = 1; i < 2; i++) {
+	for (var i = 1; i < 3; i++) {
 		states[0][i] <== 0;
 	}
 
 	for (var i = 0; i < num_bytes; i++) {
-		state_changed[i] = MultiOR(1);
+		state_changed[i] = MultiOR(2);
 		states[i][0] <== 1;
 		eq[0][i] = IsEqual();
 		eq[0][i].in[0] <== in[i];
-		eq[0][i].in[1] <== 97;
+		eq[0][i].in[1] <== 255;
+		and[0][i] = AND();
+		and[0][i].a <== states[i][0];
+		and[0][i].b <== eq[0][i].out;
+		states_tmp[i+1][1] <== 0;
 		eq[1][i] = IsEqual();
 		eq[1][i].in[0] <== in[i];
-		eq[1][i].in[1] <== 98;
+		eq[1][i].in[1] <== 97;
 		eq[2][i] = IsEqual();
 		eq[2][i].in[0] <== in[i];
-		eq[2][i].in[1] <== 99;
-		and[0][i] = AND();
-		and[0][i].a <== states[i][0];
+		eq[2][i].in[1] <== 98;
+		eq[3][i] = IsEqual();
+		eq[3][i].in[0] <== in[i];
+		eq[3][i].in[1] <== 99;
+		and[1][i] = AND();
+		and[1][i].a <== states[i][1];
 		multi_or[0][i] = MultiOR(3);
-		multi_or[0][i].in[0] <== eq[0][i].out;
-		multi_or[0][i].in[1] <== eq[1][i].out;
-		multi_or[0][i].in[2] <== eq[2][i].out;
-		and[0][i].b <== multi_or[0][i].out;
-		states_tmp[i+1][1] <== 0;
-		from_zero_enabled[i] <== MultiNOR(1)([states_tmp[i+1][1]]);
+		multi_or[0][i].in[0] <== eq[1][i].out;
+		multi_or[0][i].in[1] <== eq[2][i].out;
+		multi_or[0][i].in[2] <== eq[3][i].out;
+		and[1][i].b <== multi_or[0][i].out;
+		states[i+1][2] <== and[1][i].out;
+		from_zero_enabled[i] <== MultiNOR(2)([states_tmp[i+1][1], states[i+1][2]]);
 		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[0][i].out]);
 		state_changed[i].in[0] <== states[i+1][1];
+		state_changed[i].in[1] <== states[i+1][2];
 	}
 
 	component final_state_result = MultiOR(num_bytes+1);
 	for (var i = 0; i <= num_bytes; i++) {
-		final_state_result.in[i] <== states[i][1];
+		final_state_result.in[i] <== states[i][2];
 	}
 	out <== final_state_result.out;
 	signal is_consecutive[msg_bytes+1][3];
 	is_consecutive[msg_bytes][2] <== 0;
 	for (var i = 0; i < msg_bytes; i++) {
-		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][1] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
+		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][2] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
 		is_consecutive[msg_bytes-1-i][1] <== state_changed[msg_bytes-i].out * is_consecutive[msg_bytes-1-i][0];
-		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][1], is_consecutive[msg_bytes-1-i][1]]);
+		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][2], is_consecutive[msg_bytes-1-i][1]]);
 	}
-	// substrings calculated: [{(0, 1)}]
+	// substrings calculated: [{(1, 2)}]
 	signal is_substr0[msg_bytes];
 	signal is_reveal0[msg_bytes];
 	signal output reveal0[msg_bytes];
 	for (var i = 0; i < msg_bytes; i++) {
-		 // the 0-th substring transitions: [(0, 1)]
-		is_substr0[i] <== MultiOR(1)([states[i+1][0] * states[i+2][1]]);
+		 // the 0-th substring transitions: [(1, 2)]
+		is_substr0[i] <== MultiOR(1)([states[i+1][1] * states[i+2][2]]);
 		is_reveal0[i] <== is_substr0[i] * is_consecutive[i][2];
 		reveal0[i] <== in[i+1] * is_reveal0[i];
 	}
diff --git a/packages/circom/tests/circuits/caret3.json b/packages/circom/tests/circuits/caret3.json
index 23a77bd..8d1c6e6 100644
--- a/packages/circom/tests/circuits/caret3.json
+++ b/packages/circom/tests/circuits/caret3.json
@@ -1,8 +1,12 @@
 {
     "parts": [
+        {
+            "is_public": false,
+            "regex_def": "(^|a)"
+        },
         {
             "is_public": true,
-            "regex_def": "^.+"
+            "regex_def": "b+"
         }
     ]
 }
\ No newline at end of file
diff --git a/packages/circom/tests/circuits/caret3_regex.circom b/packages/circom/tests/circuits/caret3_regex.circom
index bda330e..d692698 100644
--- a/packages/circom/tests/circuits/caret3_regex.circom
+++ b/packages/circom/tests/circuits/caret3_regex.circom
@@ -2,7 +2,7 @@ pragma circom 2.1.5;
 
 include "@zk-email/zk-regex-circom/circuits/regex_helpers.circom";
 
-// regex: ^.+
+// regex: (^|a)b+
 template Caret3Regex(msg_bytes) {
 	signal input msg[msg_bytes];
 	signal output out;
@@ -14,394 +14,73 @@ template Caret3Regex(msg_bytes) {
 		in[i+1] <== msg[i];
 	}
 
-	component eq[47][num_bytes];
-	component lt[12][num_bytes];
-	component and[29][num_bytes];
-	component multi_or[7][num_bytes];
-	signal states[num_bytes+1][9];
-	signal states_tmp[num_bytes+1][9];
+	component eq[3][num_bytes];
+	component and[3][num_bytes];
+	component multi_or[2][num_bytes];
+	signal states[num_bytes+1][3];
+	signal states_tmp[num_bytes+1][3];
 	signal from_zero_enabled[num_bytes+1];
 	from_zero_enabled[num_bytes] <== 0;
 	component state_changed[num_bytes];
 
-	for (var i = 1; i < 9; i++) {
+	for (var i = 1; i < 3; i++) {
 		states[0][i] <== 0;
 	}
 
 	for (var i = 0; i < num_bytes; i++) {
-		state_changed[i] = MultiOR(8);
+		state_changed[i] = MultiOR(2);
 		states[i][0] <== 1;
-		lt[0][i] = LessEqThan(8);
-		lt[0][i].in[0] <== 194;
-		lt[0][i].in[1] <== in[i];
-		lt[1][i] = LessEqThan(8);
-		lt[1][i].in[0] <== in[i];
-		lt[1][i].in[1] <== 223;
-		and[0][i] = AND();
-		and[0][i].a <== lt[0][i].out;
-		and[0][i].b <== lt[1][i].out;
-		and[1][i] = AND();
-		and[1][i].a <== states[i][0];
-		and[1][i].b <== and[0][i].out;
-		lt[2][i] = LessEqThan(8);
-		lt[2][i].in[0] <== 160;
-		lt[2][i].in[1] <== in[i];
-		lt[3][i] = LessEqThan(8);
-		lt[3][i].in[0] <== in[i];
-		lt[3][i].in[1] <== 191;
-		and[2][i] = AND();
-		and[2][i].a <== lt[2][i].out;
-		and[2][i].b <== lt[3][i].out;
-		and[3][i] = AND();
-		and[3][i].a <== states[i][2];
-		and[3][i].b <== and[2][i].out;
-		lt[4][i] = LessEqThan(8);
-		lt[4][i].in[0] <== 128;
-		lt[4][i].in[1] <== in[i];
-		lt[5][i] = LessEqThan(8);
-		lt[5][i].in[0] <== in[i];
-		lt[5][i].in[1] <== 191;
-		and[4][i] = AND();
-		and[4][i].a <== lt[4][i].out;
-		and[4][i].b <== lt[5][i].out;
-		and[5][i] = AND();
-		and[5][i].a <== states[i][3];
-		and[5][i].b <== and[4][i].out;
-		lt[6][i] = LessEqThan(8);
-		lt[6][i].in[0] <== 128;
-		lt[6][i].in[1] <== in[i];
-		lt[7][i] = LessEqThan(8);
-		lt[7][i].in[0] <== in[i];
-		lt[7][i].in[1] <== 159;
-		and[6][i] = AND();
-		and[6][i].a <== lt[6][i].out;
-		and[6][i].b <== lt[7][i].out;
-		and[7][i] = AND();
-		and[7][i].a <== states[i][4];
-		and[7][i].b <== and[6][i].out;
-		and[8][i] = AND();
-		and[8][i].a <== states[i][8];
-		and[8][i].b <== and[0][i].out;
-		multi_or[0][i] = MultiOR(4);
-		multi_or[0][i].in[0] <== and[3][i].out;
-		multi_or[0][i].in[1] <== and[5][i].out;
-		multi_or[0][i].in[2] <== and[7][i].out;
-		multi_or[0][i].in[3] <== and[8][i].out;
-		states_tmp[i+1][1] <== multi_or[0][i].out;
 		eq[0][i] = IsEqual();
 		eq[0][i].in[0] <== in[i];
-		eq[0][i].in[1] <== 224;
-		and[9][i] = AND();
-		and[9][i].a <== states[i][0];
-		and[9][i].b <== eq[0][i].out;
-		and[10][i] = AND();
-		and[10][i].a <== states[i][8];
-		and[10][i].b <== eq[0][i].out;
-		states_tmp[i+1][2] <== and[10][i].out;
+		eq[0][i].in[1] <== 97;
 		eq[1][i] = IsEqual();
 		eq[1][i].in[0] <== in[i];
-		eq[1][i].in[1] <== 225;
+		eq[1][i].in[1] <== 255;
+		and[0][i] = AND();
+		and[0][i].a <== states[i][0];
+		multi_or[0][i] = MultiOR(2);
+		multi_or[0][i].in[0] <== eq[0][i].out;
+		multi_or[0][i].in[1] <== eq[1][i].out;
+		and[0][i].b <== multi_or[0][i].out;
+		states_tmp[i+1][1] <== 0;
 		eq[2][i] = IsEqual();
 		eq[2][i].in[0] <== in[i];
-		eq[2][i].in[1] <== 226;
-		eq[3][i] = IsEqual();
-		eq[3][i].in[0] <== in[i];
-		eq[3][i].in[1] <== 227;
-		eq[4][i] = IsEqual();
-		eq[4][i].in[0] <== in[i];
-		eq[4][i].in[1] <== 228;
-		eq[5][i] = IsEqual();
-		eq[5][i].in[0] <== in[i];
-		eq[5][i].in[1] <== 229;
-		eq[6][i] = IsEqual();
-		eq[6][i].in[0] <== in[i];
-		eq[6][i].in[1] <== 230;
-		eq[7][i] = IsEqual();
-		eq[7][i].in[0] <== in[i];
-		eq[7][i].in[1] <== 231;
-		eq[8][i] = IsEqual();
-		eq[8][i].in[0] <== in[i];
-		eq[8][i].in[1] <== 232;
-		eq[9][i] = IsEqual();
-		eq[9][i].in[0] <== in[i];
-		eq[9][i].in[1] <== 233;
-		eq[10][i] = IsEqual();
-		eq[10][i].in[0] <== in[i];
-		eq[10][i].in[1] <== 234;
-		eq[11][i] = IsEqual();
-		eq[11][i].in[0] <== in[i];
-		eq[11][i].in[1] <== 235;
-		eq[12][i] = IsEqual();
-		eq[12][i].in[0] <== in[i];
-		eq[12][i].in[1] <== 236;
-		eq[13][i] = IsEqual();
-		eq[13][i].in[0] <== in[i];
-		eq[13][i].in[1] <== 238;
-		eq[14][i] = IsEqual();
-		eq[14][i].in[0] <== in[i];
-		eq[14][i].in[1] <== 239;
-		and[11][i] = AND();
-		and[11][i].a <== states[i][0];
-		multi_or[1][i] = MultiOR(14);
-		multi_or[1][i].in[0] <== eq[1][i].out;
-		multi_or[1][i].in[1] <== eq[2][i].out;
-		multi_or[1][i].in[2] <== eq[3][i].out;
-		multi_or[1][i].in[3] <== eq[4][i].out;
-		multi_or[1][i].in[4] <== eq[5][i].out;
-		multi_or[1][i].in[5] <== eq[6][i].out;
-		multi_or[1][i].in[6] <== eq[7][i].out;
-		multi_or[1][i].in[7] <== eq[8][i].out;
-		multi_or[1][i].in[8] <== eq[9][i].out;
-		multi_or[1][i].in[9] <== eq[10][i].out;
-		multi_or[1][i].in[10] <== eq[11][i].out;
-		multi_or[1][i].in[11] <== eq[12][i].out;
-		multi_or[1][i].in[12] <== eq[13][i].out;
-		multi_or[1][i].in[13] <== eq[14][i].out;
-		and[11][i].b <== multi_or[1][i].out;
-		lt[8][i] = LessEqThan(8);
-		lt[8][i].in[0] <== 144;
-		lt[8][i].in[1] <== in[i];
-		lt[9][i] = LessEqThan(8);
-		lt[9][i].in[0] <== in[i];
-		lt[9][i].in[1] <== 191;
-		and[12][i] = AND();
-		and[12][i].a <== lt[8][i].out;
-		and[12][i].b <== lt[9][i].out;
-		and[13][i] = AND();
-		and[13][i].a <== states[i][5];
-		and[13][i].b <== and[12][i].out;
-		and[14][i] = AND();
-		and[14][i].a <== states[i][6];
-		and[14][i].b <== and[4][i].out;
-		eq[15][i] = IsEqual();
-		eq[15][i].in[0] <== in[i];
-		eq[15][i].in[1] <== 128;
-		eq[16][i] = IsEqual();
-		eq[16][i].in[0] <== in[i];
-		eq[16][i].in[1] <== 129;
-		eq[17][i] = IsEqual();
-		eq[17][i].in[0] <== in[i];
-		eq[17][i].in[1] <== 130;
-		eq[18][i] = IsEqual();
-		eq[18][i].in[0] <== in[i];
-		eq[18][i].in[1] <== 131;
-		eq[19][i] = IsEqual();
-		eq[19][i].in[0] <== in[i];
-		eq[19][i].in[1] <== 132;
-		eq[20][i] = IsEqual();
-		eq[20][i].in[0] <== in[i];
-		eq[20][i].in[1] <== 133;
-		eq[21][i] = IsEqual();
-		eq[21][i].in[0] <== in[i];
-		eq[21][i].in[1] <== 134;
-		eq[22][i] = IsEqual();
-		eq[22][i].in[0] <== in[i];
-		eq[22][i].in[1] <== 135;
-		eq[23][i] = IsEqual();
-		eq[23][i].in[0] <== in[i];
-		eq[23][i].in[1] <== 136;
-		eq[24][i] = IsEqual();
-		eq[24][i].in[0] <== in[i];
-		eq[24][i].in[1] <== 137;
-		eq[25][i] = IsEqual();
-		eq[25][i].in[0] <== in[i];
-		eq[25][i].in[1] <== 138;
-		eq[26][i] = IsEqual();
-		eq[26][i].in[0] <== in[i];
-		eq[26][i].in[1] <== 139;
-		eq[27][i] = IsEqual();
-		eq[27][i].in[0] <== in[i];
-		eq[27][i].in[1] <== 140;
-		eq[28][i] = IsEqual();
-		eq[28][i].in[0] <== in[i];
-		eq[28][i].in[1] <== 141;
-		eq[29][i] = IsEqual();
-		eq[29][i].in[0] <== in[i];
-		eq[29][i].in[1] <== 142;
-		eq[30][i] = IsEqual();
-		eq[30][i].in[0] <== in[i];
-		eq[30][i].in[1] <== 143;
-		and[15][i] = AND();
-		and[15][i].a <== states[i][7];
-		multi_or[2][i] = MultiOR(16);
-		multi_or[2][i].in[0] <== eq[15][i].out;
-		multi_or[2][i].in[1] <== eq[16][i].out;
-		multi_or[2][i].in[2] <== eq[17][i].out;
-		multi_or[2][i].in[3] <== eq[18][i].out;
-		multi_or[2][i].in[4] <== eq[19][i].out;
-		multi_or[2][i].in[5] <== eq[20][i].out;
-		multi_or[2][i].in[6] <== eq[21][i].out;
-		multi_or[2][i].in[7] <== eq[22][i].out;
-		multi_or[2][i].in[8] <== eq[23][i].out;
-		multi_or[2][i].in[9] <== eq[24][i].out;
-		multi_or[2][i].in[10] <== eq[25][i].out;
-		multi_or[2][i].in[11] <== eq[26][i].out;
-		multi_or[2][i].in[12] <== eq[27][i].out;
-		multi_or[2][i].in[13] <== eq[28][i].out;
-		multi_or[2][i].in[14] <== eq[29][i].out;
-		multi_or[2][i].in[15] <== eq[30][i].out;
-		and[15][i].b <== multi_or[2][i].out;
-		and[16][i] = AND();
-		and[16][i].a <== states[i][8];
-		and[16][i].b <== multi_or[1][i].out;
-		multi_or[3][i] = MultiOR(4);
-		multi_or[3][i].in[0] <== and[13][i].out;
-		multi_or[3][i].in[1] <== and[14][i].out;
-		multi_or[3][i].in[2] <== and[15][i].out;
-		multi_or[3][i].in[3] <== and[16][i].out;
-		states_tmp[i+1][3] <== multi_or[3][i].out;
-		eq[31][i] = IsEqual();
-		eq[31][i].in[0] <== in[i];
-		eq[31][i].in[1] <== 237;
-		and[17][i] = AND();
-		and[17][i].a <== states[i][0];
-		and[17][i].b <== eq[31][i].out;
-		and[18][i] = AND();
-		and[18][i].a <== states[i][8];
-		and[18][i].b <== eq[31][i].out;
-		states_tmp[i+1][4] <== and[18][i].out;
-		eq[32][i] = IsEqual();
-		eq[32][i].in[0] <== in[i];
-		eq[32][i].in[1] <== 240;
-		and[19][i] = AND();
-		and[19][i].a <== states[i][0];
-		and[19][i].b <== eq[32][i].out;
-		and[20][i] = AND();
-		and[20][i].a <== states[i][8];
-		and[20][i].b <== eq[32][i].out;
-		states_tmp[i+1][5] <== and[20][i].out;
-		eq[33][i] = IsEqual();
-		eq[33][i].in[0] <== in[i];
-		eq[33][i].in[1] <== 241;
-		eq[34][i] = IsEqual();
-		eq[34][i].in[0] <== in[i];
-		eq[34][i].in[1] <== 242;
-		eq[35][i] = IsEqual();
-		eq[35][i].in[0] <== in[i];
-		eq[35][i].in[1] <== 243;
-		and[21][i] = AND();
-		and[21][i].a <== states[i][0];
-		multi_or[4][i] = MultiOR(3);
-		multi_or[4][i].in[0] <== eq[33][i].out;
-		multi_or[4][i].in[1] <== eq[34][i].out;
-		multi_or[4][i].in[2] <== eq[35][i].out;
-		and[21][i].b <== multi_or[4][i].out;
-		and[22][i] = AND();
-		and[22][i].a <== states[i][8];
-		and[22][i].b <== multi_or[4][i].out;
-		states_tmp[i+1][6] <== and[22][i].out;
-		eq[36][i] = IsEqual();
-		eq[36][i].in[0] <== in[i];
-		eq[36][i].in[1] <== 244;
-		and[23][i] = AND();
-		and[23][i].a <== states[i][0];
-		and[23][i].b <== eq[36][i].out;
-		and[24][i] = AND();
-		and[24][i].a <== states[i][8];
-		and[24][i].b <== eq[36][i].out;
-		states_tmp[i+1][7] <== and[24][i].out;
-		lt[10][i] = LessEqThan(8);
-		lt[10][i].in[0] <== 11;
-		lt[10][i].in[1] <== in[i];
-		lt[11][i] = LessEqThan(8);
-		lt[11][i].in[0] <== in[i];
-		lt[11][i].in[1] <== 127;
-		and[25][i] = AND();
-		and[25][i].a <== lt[10][i].out;
-		and[25][i].b <== lt[11][i].out;
-		eq[37][i] = IsEqual();
-		eq[37][i].in[0] <== in[i];
-		eq[37][i].in[1] <== 0;
-		eq[38][i] = IsEqual();
-		eq[38][i].in[0] <== in[i];
-		eq[38][i].in[1] <== 1;
-		eq[39][i] = IsEqual();
-		eq[39][i].in[0] <== in[i];
-		eq[39][i].in[1] <== 2;
-		eq[40][i] = IsEqual();
-		eq[40][i].in[0] <== in[i];
-		eq[40][i].in[1] <== 3;
-		eq[41][i] = IsEqual();
-		eq[41][i].in[0] <== in[i];
-		eq[41][i].in[1] <== 4;
-		eq[42][i] = IsEqual();
-		eq[42][i].in[0] <== in[i];
-		eq[42][i].in[1] <== 5;
-		eq[43][i] = IsEqual();
-		eq[43][i].in[0] <== in[i];
-		eq[43][i].in[1] <== 6;
-		eq[44][i] = IsEqual();
-		eq[44][i].in[0] <== in[i];
-		eq[44][i].in[1] <== 7;
-		eq[45][i] = IsEqual();
-		eq[45][i].in[0] <== in[i];
-		eq[45][i].in[1] <== 8;
-		eq[46][i] = IsEqual();
-		eq[46][i].in[0] <== in[i];
-		eq[46][i].in[1] <== 9;
-		and[26][i] = AND();
-		and[26][i].a <== states[i][0];
-		multi_or[5][i] = MultiOR(11);
-		multi_or[5][i].in[0] <== and[25][i].out;
-		multi_or[5][i].in[1] <== eq[37][i].out;
-		multi_or[5][i].in[2] <== eq[38][i].out;
-		multi_or[5][i].in[3] <== eq[39][i].out;
-		multi_or[5][i].in[4] <== eq[40][i].out;
-		multi_or[5][i].in[5] <== eq[41][i].out;
-		multi_or[5][i].in[6] <== eq[42][i].out;
-		multi_or[5][i].in[7] <== eq[43][i].out;
-		multi_or[5][i].in[8] <== eq[44][i].out;
-		multi_or[5][i].in[9] <== eq[45][i].out;
-		multi_or[5][i].in[10] <== eq[46][i].out;
-		and[26][i].b <== multi_or[5][i].out;
-		and[27][i] = AND();
-		and[27][i].a <== states[i][1];
-		and[27][i].b <== and[4][i].out;
-		and[28][i] = AND();
-		and[28][i].a <== states[i][8];
-		and[28][i].b <== multi_or[5][i].out;
-		multi_or[6][i] = MultiOR(2);
-		multi_or[6][i].in[0] <== and[27][i].out;
-		multi_or[6][i].in[1] <== and[28][i].out;
-		states_tmp[i+1][8] <== multi_or[6][i].out;
-		from_zero_enabled[i] <== MultiNOR(8)([states_tmp[i+1][1], states_tmp[i+1][2], states_tmp[i+1][3], states_tmp[i+1][4], states_tmp[i+1][5], states_tmp[i+1][6], states_tmp[i+1][7], states_tmp[i+1][8]]);
-		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[1][i].out]);
-		states[i+1][2] <== MultiOR(2)([states_tmp[i+1][2], from_zero_enabled[i] * and[9][i].out]);
-		states[i+1][3] <== MultiOR(2)([states_tmp[i+1][3], from_zero_enabled[i] * and[11][i].out]);
-		states[i+1][4] <== MultiOR(2)([states_tmp[i+1][4], from_zero_enabled[i] * and[17][i].out]);
-		states[i+1][5] <== MultiOR(2)([states_tmp[i+1][5], from_zero_enabled[i] * and[19][i].out]);
-		states[i+1][6] <== MultiOR(2)([states_tmp[i+1][6], from_zero_enabled[i] * and[21][i].out]);
-		states[i+1][7] <== MultiOR(2)([states_tmp[i+1][7], from_zero_enabled[i] * and[23][i].out]);
-		states[i+1][8] <== MultiOR(2)([states_tmp[i+1][8], from_zero_enabled[i] * and[26][i].out]);
+		eq[2][i].in[1] <== 98;
+		and[1][i] = AND();
+		and[1][i].a <== states[i][1];
+		and[1][i].b <== eq[2][i].out;
+		and[2][i] = AND();
+		and[2][i].a <== states[i][2];
+		and[2][i].b <== eq[2][i].out;
+		multi_or[1][i] = MultiOR(2);
+		multi_or[1][i].in[0] <== and[1][i].out;
+		multi_or[1][i].in[1] <== and[2][i].out;
+		states[i+1][2] <== multi_or[1][i].out;
+		from_zero_enabled[i] <== MultiNOR(2)([states_tmp[i+1][1], states[i+1][2]]);
+		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[0][i].out]);
 		state_changed[i].in[0] <== states[i+1][1];
 		state_changed[i].in[1] <== states[i+1][2];
-		state_changed[i].in[2] <== states[i+1][3];
-		state_changed[i].in[3] <== states[i+1][4];
-		state_changed[i].in[4] <== states[i+1][5];
-		state_changed[i].in[5] <== states[i+1][6];
-		state_changed[i].in[6] <== states[i+1][7];
-		state_changed[i].in[7] <== states[i+1][8];
 	}
 
 	component final_state_result = MultiOR(num_bytes+1);
 	for (var i = 0; i <= num_bytes; i++) {
-		final_state_result.in[i] <== states[i][8];
+		final_state_result.in[i] <== states[i][2];
 	}
 	out <== final_state_result.out;
 	signal is_consecutive[msg_bytes+1][3];
 	is_consecutive[msg_bytes][2] <== 0;
 	for (var i = 0; i < msg_bytes; i++) {
-		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][8] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
+		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][2] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
 		is_consecutive[msg_bytes-1-i][1] <== state_changed[msg_bytes-i].out * is_consecutive[msg_bytes-1-i][0];
-		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][8], is_consecutive[msg_bytes-1-i][1]]);
+		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][2], is_consecutive[msg_bytes-1-i][1]]);
 	}
-	// substrings calculated: [{(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (1, 8), (2, 1), (3, 1), (4, 1), (5, 3), (6, 3), (7, 3), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8)}]
+	// substrings calculated: [{(1, 2), (2, 2)}]
 	signal is_substr0[msg_bytes];
 	signal is_reveal0[msg_bytes];
 	signal output reveal0[msg_bytes];
 	for (var i = 0; i < msg_bytes; i++) {
-		 // the 0-th substring transitions: [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (1, 8), (2, 1), (3, 1), (4, 1), (5, 3), (6, 3), (7, 3), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8)]
-		is_substr0[i] <== MultiOR(23)([states[i+1][0] * states[i+2][1], states[i+1][0] * states[i+2][2], states[i+1][0] * states[i+2][3], states[i+1][0] * states[i+2][4], states[i+1][0] * states[i+2][5], states[i+1][0] * states[i+2][6], states[i+1][0] * states[i+2][7], states[i+1][0] * states[i+2][8], states[i+1][1] * states[i+2][8], states[i+1][2] * states[i+2][1], states[i+1][3] * states[i+2][1], states[i+1][4] * states[i+2][1], states[i+1][5] * states[i+2][3], states[i+1][6] * states[i+2][3], states[i+1][7] * states[i+2][3], states[i+1][8] * states[i+2][1], states[i+1][8] * states[i+2][2], states[i+1][8] * states[i+2][3], states[i+1][8] * states[i+2][4], states[i+1][8] * states[i+2][5], states[i+1][8] * states[i+2][6], states[i+1][8] * states[i+2][7], states[i+1][8] * states[i+2][8]]);
+		 // the 0-th substring transitions: [(1, 2), (2, 2)]
+		is_substr0[i] <== MultiOR(2)([states[i+1][1] * states[i+2][2], states[i+1][2] * states[i+2][2]]);
 		is_reveal0[i] <== is_substr0[i] * is_consecutive[i][2];
 		reveal0[i] <== in[i+1] * is_reveal0[i];
 	}
diff --git a/packages/circom/tests/circuits/caret4.json b/packages/circom/tests/circuits/caret4.json
index 5ee7493..a8d097f 100644
--- a/packages/circom/tests/circuits/caret4.json
+++ b/packages/circom/tests/circuits/caret4.json
@@ -1,8 +1,12 @@
 {
     "parts": [
+        {
+            "is_public": false,
+            "regex_def": "(\n|^)x"
+        },
         {
             "is_public": true,
-            "regex_def": "(\n|^)(a|b)+"
+            "regex_def": "(a|b)+"
         }
     ]
 }
\ No newline at end of file
diff --git a/packages/circom/tests/circuits/caret4_regex.circom b/packages/circom/tests/circuits/caret4_regex.circom
index b906945..73e8524 100644
--- a/packages/circom/tests/circuits/caret4_regex.circom
+++ b/packages/circom/tests/circuits/caret4_regex.circom
@@ -2,7 +2,7 @@ pragma circom 2.1.5;
 
 include "@zk-email/zk-regex-circom/circuits/regex_helpers.circom";
 
-// regex: (\n|^)(a|b)+
+// regex: (\n|^)x(a|b)+
 template Caret4Regex(msg_bytes) {
 	signal input msg[msg_bytes];
 	signal output out;
@@ -14,77 +14,87 @@ template Caret4Regex(msg_bytes) {
 		in[i+1] <== msg[i];
 	}
 
-	component eq[3][num_bytes];
+	component eq[5][num_bytes];
 	component and[4][num_bytes];
-	component multi_or[2][num_bytes];
-	signal states[num_bytes+1][3];
-	signal states_tmp[num_bytes+1][3];
+	component multi_or[3][num_bytes];
+	signal states[num_bytes+1][4];
+	signal states_tmp[num_bytes+1][4];
 	signal from_zero_enabled[num_bytes+1];
 	from_zero_enabled[num_bytes] <== 0;
 	component state_changed[num_bytes];
 
-	for (var i = 1; i < 3; i++) {
+	for (var i = 1; i < 4; i++) {
 		states[0][i] <== 0;
 	}
 
 	for (var i = 0; i < num_bytes; i++) {
-		state_changed[i] = MultiOR(2);
+		state_changed[i] = MultiOR(3);
 		states[i][0] <== 1;
 		eq[0][i] = IsEqual();
 		eq[0][i].in[0] <== in[i];
-		eq[0][i].in[1] <== 97;
+		eq[0][i].in[1] <== 10;
 		eq[1][i] = IsEqual();
 		eq[1][i].in[0] <== in[i];
-		eq[1][i].in[1] <== 98;
+		eq[1][i].in[1] <== 255;
 		and[0][i] = AND();
 		and[0][i].a <== states[i][0];
 		multi_or[0][i] = MultiOR(2);
 		multi_or[0][i].in[0] <== eq[0][i].out;
 		multi_or[0][i].in[1] <== eq[1][i].out;
 		and[0][i].b <== multi_or[0][i].out;
+		states_tmp[i+1][1] <== 0;
+		eq[2][i] = IsEqual();
+		eq[2][i].in[0] <== in[i];
+		eq[2][i].in[1] <== 120;
 		and[1][i] = AND();
 		and[1][i].a <== states[i][1];
-		and[1][i].b <== multi_or[0][i].out;
+		and[1][i].b <== eq[2][i].out;
+		states[i+1][2] <== and[1][i].out;
+		eq[3][i] = IsEqual();
+		eq[3][i].in[0] <== in[i];
+		eq[3][i].in[1] <== 97;
+		eq[4][i] = IsEqual();
+		eq[4][i].in[0] <== in[i];
+		eq[4][i].in[1] <== 98;
 		and[2][i] = AND();
 		and[2][i].a <== states[i][2];
-		and[2][i].b <== multi_or[0][i].out;
 		multi_or[1][i] = MultiOR(2);
-		multi_or[1][i].in[0] <== and[1][i].out;
-		multi_or[1][i].in[1] <== and[2][i].out;
-		states_tmp[i+1][1] <== multi_or[1][i].out;
-		eq[2][i] = IsEqual();
-		eq[2][i].in[0] <== in[i];
-		eq[2][i].in[1] <== 10;
+		multi_or[1][i].in[0] <== eq[3][i].out;
+		multi_or[1][i].in[1] <== eq[4][i].out;
+		and[2][i].b <== multi_or[1][i].out;
 		and[3][i] = AND();
-		and[3][i].a <== states[i][0];
-		and[3][i].b <== eq[2][i].out;
-		states_tmp[i+1][2] <== 0;
-		from_zero_enabled[i] <== MultiNOR(2)([states_tmp[i+1][1], states_tmp[i+1][2]]);
+		and[3][i].a <== states[i][3];
+		and[3][i].b <== multi_or[1][i].out;
+		multi_or[2][i] = MultiOR(2);
+		multi_or[2][i].in[0] <== and[2][i].out;
+		multi_or[2][i].in[1] <== and[3][i].out;
+		states[i+1][3] <== multi_or[2][i].out;
+		from_zero_enabled[i] <== MultiNOR(3)([states_tmp[i+1][1], states[i+1][2], states[i+1][3]]);
 		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[0][i].out]);
-		states[i+1][2] <== MultiOR(2)([states_tmp[i+1][2], from_zero_enabled[i] * and[3][i].out]);
 		state_changed[i].in[0] <== states[i+1][1];
 		state_changed[i].in[1] <== states[i+1][2];
+		state_changed[i].in[2] <== states[i+1][3];
 	}
 
 	component final_state_result = MultiOR(num_bytes+1);
 	for (var i = 0; i <= num_bytes; i++) {
-		final_state_result.in[i] <== states[i][1];
+		final_state_result.in[i] <== states[i][3];
 	}
 	out <== final_state_result.out;
 	signal is_consecutive[msg_bytes+1][3];
 	is_consecutive[msg_bytes][2] <== 0;
 	for (var i = 0; i < msg_bytes; i++) {
-		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][1] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
+		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][3] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
 		is_consecutive[msg_bytes-1-i][1] <== state_changed[msg_bytes-i].out * is_consecutive[msg_bytes-1-i][0];
-		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][1], is_consecutive[msg_bytes-1-i][1]]);
+		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][3], is_consecutive[msg_bytes-1-i][1]]);
 	}
-	// substrings calculated: [{(0, 1), (0, 2), (1, 1), (2, 1)}]
+	// substrings calculated: [{(2, 3), (3, 3)}]
 	signal is_substr0[msg_bytes];
 	signal is_reveal0[msg_bytes];
 	signal output reveal0[msg_bytes];
 	for (var i = 0; i < msg_bytes; i++) {
-		 // the 0-th substring transitions: [(0, 1), (0, 2), (1, 1), (2, 1)]
-		is_substr0[i] <== MultiOR(4)([states[i+1][0] * states[i+2][1], states[i+1][0] * states[i+2][2], states[i+1][1] * states[i+2][1], states[i+1][2] * states[i+2][1]]);
+		 // the 0-th substring transitions: [(2, 3), (3, 3)]
+		is_substr0[i] <== MultiOR(2)([states[i+1][2] * states[i+2][3], states[i+1][3] * states[i+2][3]]);
 		is_reveal0[i] <== is_substr0[i] * is_consecutive[i][2];
 		reveal0[i] <== in[i+1] * is_reveal0[i];
 	}
diff --git a/packages/circom/tests/circuits/caret5.json b/packages/circom/tests/circuits/caret5.json
index ccb614e..6d18627 100644
--- a/packages/circom/tests/circuits/caret5.json
+++ b/packages/circom/tests/circuits/caret5.json
@@ -1,8 +1,12 @@
 {
     "parts": [
+        {
+            "is_public": false,
+            "regex_def": "(\n|^)x"
+        },
         {
             "is_public": true,
-            "regex_def": "(\n|^)[^abc]+"
+            "regex_def": "[^abc]+"
         }
     ]
 }
\ No newline at end of file
diff --git a/packages/circom/tests/circuits/caret5_regex.circom b/packages/circom/tests/circuits/caret5_regex.circom
index a60bf6f..dbde513 100644
--- a/packages/circom/tests/circuits/caret5_regex.circom
+++ b/packages/circom/tests/circuits/caret5_regex.circom
@@ -2,7 +2,7 @@ pragma circom 2.1.5;
 
 include "@zk-email/zk-regex-circom/circuits/regex_helpers.circom";
 
-// regex: (\n|^)[^abc]+
+// regex: (\n|^)x[^abc]+
 template Caret5Regex(msg_bytes) {
 	signal input msg[msg_bytes];
 	signal output out;
@@ -14,335 +14,366 @@ template Caret5Regex(msg_bytes) {
 		in[i+1] <== msg[i];
 	}
 
-	component eq[37][num_bytes];
+	component eq[40][num_bytes];
 	component lt[14][num_bytes];
-	component and[30][num_bytes];
-	component multi_or[7][num_bytes];
-	signal states[num_bytes+1][9];
-	signal states_tmp[num_bytes+1][9];
+	component and[32][num_bytes];
+	component multi_or[13][num_bytes];
+	signal states[num_bytes+1][11];
+	signal states_tmp[num_bytes+1][11];
 	signal from_zero_enabled[num_bytes+1];
 	from_zero_enabled[num_bytes] <== 0;
 	component state_changed[num_bytes];
 
-	for (var i = 1; i < 9; i++) {
+	for (var i = 1; i < 11; i++) {
 		states[0][i] <== 0;
 	}
 
 	for (var i = 0; i < num_bytes; i++) {
-		state_changed[i] = MultiOR(8);
+		state_changed[i] = MultiOR(10);
 		states[i][0] <== 1;
+		eq[0][i] = IsEqual();
+		eq[0][i].in[0] <== in[i];
+		eq[0][i].in[1] <== 10;
+		eq[1][i] = IsEqual();
+		eq[1][i].in[0] <== in[i];
+		eq[1][i].in[1] <== 255;
+		and[0][i] = AND();
+		and[0][i].a <== states[i][0];
+		multi_or[0][i] = MultiOR(2);
+		multi_or[0][i].in[0] <== eq[0][i].out;
+		multi_or[0][i].in[1] <== eq[1][i].out;
+		and[0][i].b <== multi_or[0][i].out;
+		states_tmp[i+1][1] <== 0;
+		eq[2][i] = IsEqual();
+		eq[2][i].in[0] <== in[i];
+		eq[2][i].in[1] <== 120;
+		and[1][i] = AND();
+		and[1][i].a <== states[i][1];
+		and[1][i].b <== eq[2][i].out;
+		states[i+1][2] <== and[1][i].out;
 		lt[0][i] = LessEqThan(8);
-		lt[0][i].in[0] <== 0;
+		lt[0][i].in[0] <== 194;
 		lt[0][i].in[1] <== in[i];
 		lt[1][i] = LessEqThan(8);
 		lt[1][i].in[0] <== in[i];
-		lt[1][i].in[1] <== 96;
-		and[0][i] = AND();
-		and[0][i].a <== lt[0][i].out;
-		and[0][i].b <== lt[1][i].out;
+		lt[1][i].in[1] <== 223;
+		and[2][i] = AND();
+		and[2][i].a <== lt[0][i].out;
+		and[2][i].b <== lt[1][i].out;
+		and[3][i] = AND();
+		and[3][i].a <== states[i][2];
+		and[3][i].b <== and[2][i].out;
 		lt[2][i] = LessEqThan(8);
-		lt[2][i].in[0] <== 100;
+		lt[2][i].in[0] <== 160;
 		lt[2][i].in[1] <== in[i];
 		lt[3][i] = LessEqThan(8);
 		lt[3][i].in[0] <== in[i];
-		lt[3][i].in[1] <== 127;
-		and[1][i] = AND();
-		and[1][i].a <== lt[2][i].out;
-		and[1][i].b <== lt[3][i].out;
-		and[2][i] = AND();
-		and[2][i].a <== states[i][0];
-		multi_or[0][i] = MultiOR(2);
-		multi_or[0][i].in[0] <== and[0][i].out;
-		multi_or[0][i].in[1] <== and[1][i].out;
-		and[2][i].b <== multi_or[0][i].out;
-		and[3][i] = AND();
-		and[3][i].a <== states[i][1];
-		and[3][i].b <== multi_or[0][i].out;
+		lt[3][i].in[1] <== 191;
+		and[4][i] = AND();
+		and[4][i].a <== lt[2][i].out;
+		and[4][i].b <== lt[3][i].out;
+		and[5][i] = AND();
+		and[5][i].a <== states[i][4];
+		and[5][i].b <== and[4][i].out;
 		lt[4][i] = LessEqThan(8);
 		lt[4][i].in[0] <== 128;
 		lt[4][i].in[1] <== in[i];
 		lt[5][i] = LessEqThan(8);
 		lt[5][i].in[0] <== in[i];
 		lt[5][i].in[1] <== 191;
-		and[4][i] = AND();
-		and[4][i].a <== lt[4][i].out;
-		and[4][i].b <== lt[5][i].out;
-		and[5][i] = AND();
-		and[5][i].a <== states[i][2];
-		and[5][i].b <== and[4][i].out;
-		multi_or[1][i] = MultiOR(2);
-		multi_or[1][i].in[0] <== and[3][i].out;
-		multi_or[1][i].in[1] <== and[5][i].out;
-		states_tmp[i+1][1] <== multi_or[1][i].out;
+		and[6][i] = AND();
+		and[6][i].a <== lt[4][i].out;
+		and[6][i].b <== lt[5][i].out;
+		and[7][i] = AND();
+		and[7][i].a <== states[i][5];
+		and[7][i].b <== and[6][i].out;
 		lt[6][i] = LessEqThan(8);
-		lt[6][i].in[0] <== 194;
+		lt[6][i].in[0] <== 128;
 		lt[6][i].in[1] <== in[i];
 		lt[7][i] = LessEqThan(8);
 		lt[7][i].in[0] <== in[i];
-		lt[7][i].in[1] <== 223;
-		and[6][i] = AND();
-		and[6][i].a <== lt[6][i].out;
-		and[6][i].b <== lt[7][i].out;
-		and[7][i] = AND();
-		and[7][i].a <== states[i][0];
-		and[7][i].b <== and[6][i].out;
+		lt[7][i].in[1] <== 159;
 		and[8][i] = AND();
-		and[8][i].a <== states[i][1];
-		and[8][i].b <== and[6][i].out;
-		lt[8][i] = LessEqThan(8);
-		lt[8][i].in[0] <== 160;
-		lt[8][i].in[1] <== in[i];
-		lt[9][i] = LessEqThan(8);
-		lt[9][i].in[0] <== in[i];
-		lt[9][i].in[1] <== 191;
+		and[8][i].a <== lt[6][i].out;
+		and[8][i].b <== lt[7][i].out;
 		and[9][i] = AND();
-		and[9][i].a <== lt[8][i].out;
-		and[9][i].b <== lt[9][i].out;
+		and[9][i].a <== states[i][6];
+		and[9][i].b <== and[8][i].out;
 		and[10][i] = AND();
-		and[10][i].a <== states[i][3];
-		and[10][i].b <== and[9][i].out;
-		and[11][i] = AND();
-		and[11][i].a <== states[i][4];
-		and[11][i].b <== and[4][i].out;
-		lt[10][i] = LessEqThan(8);
-		lt[10][i].in[0] <== 128;
-		lt[10][i].in[1] <== in[i];
-		lt[11][i] = LessEqThan(8);
-		lt[11][i].in[0] <== in[i];
-		lt[11][i].in[1] <== 159;
-		and[12][i] = AND();
-		and[12][i].a <== lt[10][i].out;
-		and[12][i].b <== lt[11][i].out;
-		and[13][i] = AND();
-		and[13][i].a <== states[i][5];
-		and[13][i].b <== and[12][i].out;
-		multi_or[2][i] = MultiOR(4);
-		multi_or[2][i].in[0] <== and[8][i].out;
-		multi_or[2][i].in[1] <== and[10][i].out;
-		multi_or[2][i].in[2] <== and[11][i].out;
-		multi_or[2][i].in[3] <== and[13][i].out;
-		states_tmp[i+1][2] <== multi_or[2][i].out;
-		eq[0][i] = IsEqual();
-		eq[0][i].in[0] <== in[i];
-		eq[0][i].in[1] <== 224;
-		and[14][i] = AND();
-		and[14][i].a <== states[i][0];
-		and[14][i].b <== eq[0][i].out;
-		and[15][i] = AND();
-		and[15][i].a <== states[i][1];
-		and[15][i].b <== eq[0][i].out;
-		states_tmp[i+1][3] <== and[15][i].out;
-		eq[1][i] = IsEqual();
-		eq[1][i].in[0] <== in[i];
-		eq[1][i].in[1] <== 225;
-		eq[2][i] = IsEqual();
-		eq[2][i].in[0] <== in[i];
-		eq[2][i].in[1] <== 226;
+		and[10][i].a <== states[i][10];
+		and[10][i].b <== and[2][i].out;
+		multi_or[1][i] = MultiOR(5);
+		multi_or[1][i].in[0] <== and[3][i].out;
+		multi_or[1][i].in[1] <== and[5][i].out;
+		multi_or[1][i].in[2] <== and[7][i].out;
+		multi_or[1][i].in[3] <== and[9][i].out;
+		multi_or[1][i].in[4] <== and[10][i].out;
+		states[i+1][3] <== multi_or[1][i].out;
 		eq[3][i] = IsEqual();
 		eq[3][i].in[0] <== in[i];
-		eq[3][i].in[1] <== 227;
+		eq[3][i].in[1] <== 224;
+		and[11][i] = AND();
+		and[11][i].a <== states[i][2];
+		and[11][i].b <== eq[3][i].out;
+		and[12][i] = AND();
+		and[12][i].a <== states[i][10];
+		and[12][i].b <== eq[3][i].out;
+		multi_or[2][i] = MultiOR(2);
+		multi_or[2][i].in[0] <== and[11][i].out;
+		multi_or[2][i].in[1] <== and[12][i].out;
+		states[i+1][4] <== multi_or[2][i].out;
 		eq[4][i] = IsEqual();
 		eq[4][i].in[0] <== in[i];
-		eq[4][i].in[1] <== 228;
+		eq[4][i].in[1] <== 225;
 		eq[5][i] = IsEqual();
 		eq[5][i].in[0] <== in[i];
-		eq[5][i].in[1] <== 229;
+		eq[5][i].in[1] <== 226;
 		eq[6][i] = IsEqual();
 		eq[6][i].in[0] <== in[i];
-		eq[6][i].in[1] <== 230;
+		eq[6][i].in[1] <== 227;
 		eq[7][i] = IsEqual();
 		eq[7][i].in[0] <== in[i];
-		eq[7][i].in[1] <== 231;
+		eq[7][i].in[1] <== 228;
 		eq[8][i] = IsEqual();
 		eq[8][i].in[0] <== in[i];
-		eq[8][i].in[1] <== 232;
+		eq[8][i].in[1] <== 229;
 		eq[9][i] = IsEqual();
 		eq[9][i].in[0] <== in[i];
-		eq[9][i].in[1] <== 233;
+		eq[9][i].in[1] <== 230;
 		eq[10][i] = IsEqual();
 		eq[10][i].in[0] <== in[i];
-		eq[10][i].in[1] <== 234;
+		eq[10][i].in[1] <== 231;
 		eq[11][i] = IsEqual();
 		eq[11][i].in[0] <== in[i];
-		eq[11][i].in[1] <== 235;
+		eq[11][i].in[1] <== 232;
 		eq[12][i] = IsEqual();
 		eq[12][i].in[0] <== in[i];
-		eq[12][i].in[1] <== 236;
+		eq[12][i].in[1] <== 233;
 		eq[13][i] = IsEqual();
 		eq[13][i].in[0] <== in[i];
-		eq[13][i].in[1] <== 238;
+		eq[13][i].in[1] <== 234;
 		eq[14][i] = IsEqual();
 		eq[14][i].in[0] <== in[i];
-		eq[14][i].in[1] <== 239;
-		and[16][i] = AND();
-		and[16][i].a <== states[i][0];
-		multi_or[3][i] = MultiOR(14);
-		multi_or[3][i].in[0] <== eq[1][i].out;
-		multi_or[3][i].in[1] <== eq[2][i].out;
-		multi_or[3][i].in[2] <== eq[3][i].out;
-		multi_or[3][i].in[3] <== eq[4][i].out;
-		multi_or[3][i].in[4] <== eq[5][i].out;
-		multi_or[3][i].in[5] <== eq[6][i].out;
-		multi_or[3][i].in[6] <== eq[7][i].out;
-		multi_or[3][i].in[7] <== eq[8][i].out;
-		multi_or[3][i].in[8] <== eq[9][i].out;
-		multi_or[3][i].in[9] <== eq[10][i].out;
-		multi_or[3][i].in[10] <== eq[11][i].out;
-		multi_or[3][i].in[11] <== eq[12][i].out;
-		multi_or[3][i].in[12] <== eq[13][i].out;
-		multi_or[3][i].in[13] <== eq[14][i].out;
-		and[16][i].b <== multi_or[3][i].out;
-		and[17][i] = AND();
-		and[17][i].a <== states[i][1];
-		and[17][i].b <== multi_or[3][i].out;
-		lt[12][i] = LessEqThan(8);
-		lt[12][i].in[0] <== 144;
-		lt[12][i].in[1] <== in[i];
-		lt[13][i] = LessEqThan(8);
-		lt[13][i].in[0] <== in[i];
-		lt[13][i].in[1] <== 191;
-		and[18][i] = AND();
-		and[18][i].a <== lt[12][i].out;
-		and[18][i].b <== lt[13][i].out;
-		and[19][i] = AND();
-		and[19][i].a <== states[i][6];
-		and[19][i].b <== and[18][i].out;
-		and[20][i] = AND();
-		and[20][i].a <== states[i][7];
-		and[20][i].b <== and[4][i].out;
+		eq[14][i].in[1] <== 235;
 		eq[15][i] = IsEqual();
 		eq[15][i].in[0] <== in[i];
-		eq[15][i].in[1] <== 128;
+		eq[15][i].in[1] <== 236;
 		eq[16][i] = IsEqual();
 		eq[16][i].in[0] <== in[i];
-		eq[16][i].in[1] <== 129;
+		eq[16][i].in[1] <== 238;
 		eq[17][i] = IsEqual();
 		eq[17][i].in[0] <== in[i];
-		eq[17][i].in[1] <== 130;
+		eq[17][i].in[1] <== 239;
+		and[13][i] = AND();
+		and[13][i].a <== states[i][2];
+		multi_or[3][i] = MultiOR(14);
+		multi_or[3][i].in[0] <== eq[4][i].out;
+		multi_or[3][i].in[1] <== eq[5][i].out;
+		multi_or[3][i].in[2] <== eq[6][i].out;
+		multi_or[3][i].in[3] <== eq[7][i].out;
+		multi_or[3][i].in[4] <== eq[8][i].out;
+		multi_or[3][i].in[5] <== eq[9][i].out;
+		multi_or[3][i].in[6] <== eq[10][i].out;
+		multi_or[3][i].in[7] <== eq[11][i].out;
+		multi_or[3][i].in[8] <== eq[12][i].out;
+		multi_or[3][i].in[9] <== eq[13][i].out;
+		multi_or[3][i].in[10] <== eq[14][i].out;
+		multi_or[3][i].in[11] <== eq[15][i].out;
+		multi_or[3][i].in[12] <== eq[16][i].out;
+		multi_or[3][i].in[13] <== eq[17][i].out;
+		and[13][i].b <== multi_or[3][i].out;
+		lt[8][i] = LessEqThan(8);
+		lt[8][i].in[0] <== 144;
+		lt[8][i].in[1] <== in[i];
+		lt[9][i] = LessEqThan(8);
+		lt[9][i].in[0] <== in[i];
+		lt[9][i].in[1] <== 191;
+		and[14][i] = AND();
+		and[14][i].a <== lt[8][i].out;
+		and[14][i].b <== lt[9][i].out;
+		and[15][i] = AND();
+		and[15][i].a <== states[i][7];
+		and[15][i].b <== and[14][i].out;
+		and[16][i] = AND();
+		and[16][i].a <== states[i][8];
+		and[16][i].b <== and[6][i].out;
 		eq[18][i] = IsEqual();
 		eq[18][i].in[0] <== in[i];
-		eq[18][i].in[1] <== 131;
+		eq[18][i].in[1] <== 128;
 		eq[19][i] = IsEqual();
 		eq[19][i].in[0] <== in[i];
-		eq[19][i].in[1] <== 132;
+		eq[19][i].in[1] <== 129;
 		eq[20][i] = IsEqual();
 		eq[20][i].in[0] <== in[i];
-		eq[20][i].in[1] <== 133;
+		eq[20][i].in[1] <== 130;
 		eq[21][i] = IsEqual();
 		eq[21][i].in[0] <== in[i];
-		eq[21][i].in[1] <== 134;
+		eq[21][i].in[1] <== 131;
 		eq[22][i] = IsEqual();
 		eq[22][i].in[0] <== in[i];
-		eq[22][i].in[1] <== 135;
+		eq[22][i].in[1] <== 132;
 		eq[23][i] = IsEqual();
 		eq[23][i].in[0] <== in[i];
-		eq[23][i].in[1] <== 136;
+		eq[23][i].in[1] <== 133;
 		eq[24][i] = IsEqual();
 		eq[24][i].in[0] <== in[i];
-		eq[24][i].in[1] <== 137;
+		eq[24][i].in[1] <== 134;
 		eq[25][i] = IsEqual();
 		eq[25][i].in[0] <== in[i];
-		eq[25][i].in[1] <== 138;
+		eq[25][i].in[1] <== 135;
 		eq[26][i] = IsEqual();
 		eq[26][i].in[0] <== in[i];
-		eq[26][i].in[1] <== 139;
+		eq[26][i].in[1] <== 136;
 		eq[27][i] = IsEqual();
 		eq[27][i].in[0] <== in[i];
-		eq[27][i].in[1] <== 140;
+		eq[27][i].in[1] <== 137;
 		eq[28][i] = IsEqual();
 		eq[28][i].in[0] <== in[i];
-		eq[28][i].in[1] <== 141;
+		eq[28][i].in[1] <== 138;
 		eq[29][i] = IsEqual();
 		eq[29][i].in[0] <== in[i];
-		eq[29][i].in[1] <== 142;
+		eq[29][i].in[1] <== 139;
 		eq[30][i] = IsEqual();
 		eq[30][i].in[0] <== in[i];
-		eq[30][i].in[1] <== 143;
-		and[21][i] = AND();
-		and[21][i].a <== states[i][8];
-		multi_or[4][i] = MultiOR(16);
-		multi_or[4][i].in[0] <== eq[15][i].out;
-		multi_or[4][i].in[1] <== eq[16][i].out;
-		multi_or[4][i].in[2] <== eq[17][i].out;
-		multi_or[4][i].in[3] <== eq[18][i].out;
-		multi_or[4][i].in[4] <== eq[19][i].out;
-		multi_or[4][i].in[5] <== eq[20][i].out;
-		multi_or[4][i].in[6] <== eq[21][i].out;
-		multi_or[4][i].in[7] <== eq[22][i].out;
-		multi_or[4][i].in[8] <== eq[23][i].out;
-		multi_or[4][i].in[9] <== eq[24][i].out;
-		multi_or[4][i].in[10] <== eq[25][i].out;
-		multi_or[4][i].in[11] <== eq[26][i].out;
-		multi_or[4][i].in[12] <== eq[27][i].out;
-		multi_or[4][i].in[13] <== eq[28][i].out;
-		multi_or[4][i].in[14] <== eq[29][i].out;
-		multi_or[4][i].in[15] <== eq[30][i].out;
-		and[21][i].b <== multi_or[4][i].out;
-		multi_or[5][i] = MultiOR(4);
-		multi_or[5][i].in[0] <== and[17][i].out;
-		multi_or[5][i].in[1] <== and[19][i].out;
-		multi_or[5][i].in[2] <== and[20][i].out;
-		multi_or[5][i].in[3] <== and[21][i].out;
-		states_tmp[i+1][4] <== multi_or[5][i].out;
+		eq[30][i].in[1] <== 140;
 		eq[31][i] = IsEqual();
 		eq[31][i].in[0] <== in[i];
-		eq[31][i].in[1] <== 237;
-		and[22][i] = AND();
-		and[22][i].a <== states[i][0];
-		and[22][i].b <== eq[31][i].out;
-		and[23][i] = AND();
-		and[23][i].a <== states[i][1];
-		and[23][i].b <== eq[31][i].out;
-		states_tmp[i+1][5] <== and[23][i].out;
+		eq[31][i].in[1] <== 141;
 		eq[32][i] = IsEqual();
 		eq[32][i].in[0] <== in[i];
-		eq[32][i].in[1] <== 240;
-		and[24][i] = AND();
-		and[24][i].a <== states[i][0];
-		and[24][i].b <== eq[32][i].out;
-		and[25][i] = AND();
-		and[25][i].a <== states[i][1];
-		and[25][i].b <== eq[32][i].out;
-		states_tmp[i+1][6] <== and[25][i].out;
+		eq[32][i].in[1] <== 142;
 		eq[33][i] = IsEqual();
 		eq[33][i].in[0] <== in[i];
-		eq[33][i].in[1] <== 241;
+		eq[33][i].in[1] <== 143;
+		and[17][i] = AND();
+		and[17][i].a <== states[i][9];
+		multi_or[4][i] = MultiOR(16);
+		multi_or[4][i].in[0] <== eq[18][i].out;
+		multi_or[4][i].in[1] <== eq[19][i].out;
+		multi_or[4][i].in[2] <== eq[20][i].out;
+		multi_or[4][i].in[3] <== eq[21][i].out;
+		multi_or[4][i].in[4] <== eq[22][i].out;
+		multi_or[4][i].in[5] <== eq[23][i].out;
+		multi_or[4][i].in[6] <== eq[24][i].out;
+		multi_or[4][i].in[7] <== eq[25][i].out;
+		multi_or[4][i].in[8] <== eq[26][i].out;
+		multi_or[4][i].in[9] <== eq[27][i].out;
+		multi_or[4][i].in[10] <== eq[28][i].out;
+		multi_or[4][i].in[11] <== eq[29][i].out;
+		multi_or[4][i].in[12] <== eq[30][i].out;
+		multi_or[4][i].in[13] <== eq[31][i].out;
+		multi_or[4][i].in[14] <== eq[32][i].out;
+		multi_or[4][i].in[15] <== eq[33][i].out;
+		and[17][i].b <== multi_or[4][i].out;
+		and[18][i] = AND();
+		and[18][i].a <== states[i][10];
+		and[18][i].b <== multi_or[3][i].out;
+		multi_or[5][i] = MultiOR(5);
+		multi_or[5][i].in[0] <== and[13][i].out;
+		multi_or[5][i].in[1] <== and[15][i].out;
+		multi_or[5][i].in[2] <== and[16][i].out;
+		multi_or[5][i].in[3] <== and[17][i].out;
+		multi_or[5][i].in[4] <== and[18][i].out;
+		states[i+1][5] <== multi_or[5][i].out;
 		eq[34][i] = IsEqual();
 		eq[34][i].in[0] <== in[i];
-		eq[34][i].in[1] <== 242;
+		eq[34][i].in[1] <== 237;
+		and[19][i] = AND();
+		and[19][i].a <== states[i][2];
+		and[19][i].b <== eq[34][i].out;
+		and[20][i] = AND();
+		and[20][i].a <== states[i][10];
+		and[20][i].b <== eq[34][i].out;
+		multi_or[6][i] = MultiOR(2);
+		multi_or[6][i].in[0] <== and[19][i].out;
+		multi_or[6][i].in[1] <== and[20][i].out;
+		states[i+1][6] <== multi_or[6][i].out;
 		eq[35][i] = IsEqual();
 		eq[35][i].in[0] <== in[i];
-		eq[35][i].in[1] <== 243;
-		and[26][i] = AND();
-		and[26][i].a <== states[i][0];
-		multi_or[6][i] = MultiOR(3);
-		multi_or[6][i].in[0] <== eq[33][i].out;
-		multi_or[6][i].in[1] <== eq[34][i].out;
-		multi_or[6][i].in[2] <== eq[35][i].out;
-		and[26][i].b <== multi_or[6][i].out;
-		and[27][i] = AND();
-		and[27][i].a <== states[i][1];
-		and[27][i].b <== multi_or[6][i].out;
-		states_tmp[i+1][7] <== and[27][i].out;
+		eq[35][i].in[1] <== 240;
+		and[21][i] = AND();
+		and[21][i].a <== states[i][2];
+		and[21][i].b <== eq[35][i].out;
+		and[22][i] = AND();
+		and[22][i].a <== states[i][10];
+		and[22][i].b <== eq[35][i].out;
+		multi_or[7][i] = MultiOR(2);
+		multi_or[7][i].in[0] <== and[21][i].out;
+		multi_or[7][i].in[1] <== and[22][i].out;
+		states[i+1][7] <== multi_or[7][i].out;
 		eq[36][i] = IsEqual();
 		eq[36][i].in[0] <== in[i];
-		eq[36][i].in[1] <== 244;
+		eq[36][i].in[1] <== 241;
+		eq[37][i] = IsEqual();
+		eq[37][i].in[0] <== in[i];
+		eq[37][i].in[1] <== 242;
+		eq[38][i] = IsEqual();
+		eq[38][i].in[0] <== in[i];
+		eq[38][i].in[1] <== 243;
+		and[23][i] = AND();
+		and[23][i].a <== states[i][2];
+		multi_or[8][i] = MultiOR(3);
+		multi_or[8][i].in[0] <== eq[36][i].out;
+		multi_or[8][i].in[1] <== eq[37][i].out;
+		multi_or[8][i].in[2] <== eq[38][i].out;
+		and[23][i].b <== multi_or[8][i].out;
+		and[24][i] = AND();
+		and[24][i].a <== states[i][10];
+		and[24][i].b <== multi_or[8][i].out;
+		multi_or[9][i] = MultiOR(2);
+		multi_or[9][i].in[0] <== and[23][i].out;
+		multi_or[9][i].in[1] <== and[24][i].out;
+		states[i+1][8] <== multi_or[9][i].out;
+		eq[39][i] = IsEqual();
+		eq[39][i].in[0] <== in[i];
+		eq[39][i].in[1] <== 244;
+		and[25][i] = AND();
+		and[25][i].a <== states[i][2];
+		and[25][i].b <== eq[39][i].out;
+		and[26][i] = AND();
+		and[26][i].a <== states[i][10];
+		and[26][i].b <== eq[39][i].out;
+		multi_or[10][i] = MultiOR(2);
+		multi_or[10][i].in[0] <== and[25][i].out;
+		multi_or[10][i].in[1] <== and[26][i].out;
+		states[i+1][9] <== multi_or[10][i].out;
+		lt[10][i] = LessEqThan(8);
+		lt[10][i].in[0] <== 0;
+		lt[10][i].in[1] <== in[i];
+		lt[11][i] = LessEqThan(8);
+		lt[11][i].in[0] <== in[i];
+		lt[11][i].in[1] <== 96;
+		and[27][i] = AND();
+		and[27][i].a <== lt[10][i].out;
+		and[27][i].b <== lt[11][i].out;
+		lt[12][i] = LessEqThan(8);
+		lt[12][i].in[0] <== 100;
+		lt[12][i].in[1] <== in[i];
+		lt[13][i] = LessEqThan(8);
+		lt[13][i].in[0] <== in[i];
+		lt[13][i].in[1] <== 127;
 		and[28][i] = AND();
-		and[28][i].a <== states[i][0];
-		and[28][i].b <== eq[36][i].out;
+		and[28][i].a <== lt[12][i].out;
+		and[28][i].b <== lt[13][i].out;
 		and[29][i] = AND();
-		and[29][i].a <== states[i][1];
-		and[29][i].b <== eq[36][i].out;
-		states_tmp[i+1][8] <== and[29][i].out;
-		from_zero_enabled[i] <== MultiNOR(8)([states_tmp[i+1][1], states_tmp[i+1][2], states_tmp[i+1][3], states_tmp[i+1][4], states_tmp[i+1][5], states_tmp[i+1][6], states_tmp[i+1][7], states_tmp[i+1][8]]);
-		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[2][i].out]);
-		states[i+1][2] <== MultiOR(2)([states_tmp[i+1][2], from_zero_enabled[i] * and[7][i].out]);
-		states[i+1][3] <== MultiOR(2)([states_tmp[i+1][3], from_zero_enabled[i] * and[14][i].out]);
-		states[i+1][4] <== MultiOR(2)([states_tmp[i+1][4], from_zero_enabled[i] * and[16][i].out]);
-		states[i+1][5] <== MultiOR(2)([states_tmp[i+1][5], from_zero_enabled[i] * and[22][i].out]);
-		states[i+1][6] <== MultiOR(2)([states_tmp[i+1][6], from_zero_enabled[i] * and[24][i].out]);
-		states[i+1][7] <== MultiOR(2)([states_tmp[i+1][7], from_zero_enabled[i] * and[26][i].out]);
-		states[i+1][8] <== MultiOR(2)([states_tmp[i+1][8], from_zero_enabled[i] * and[28][i].out]);
+		and[29][i].a <== states[i][2];
+		multi_or[11][i] = MultiOR(2);
+		multi_or[11][i].in[0] <== and[27][i].out;
+		multi_or[11][i].in[1] <== and[28][i].out;
+		and[29][i].b <== multi_or[11][i].out;
+		and[30][i] = AND();
+		and[30][i].a <== states[i][3];
+		and[30][i].b <== and[6][i].out;
+		and[31][i] = AND();
+		and[31][i].a <== states[i][10];
+		and[31][i].b <== multi_or[11][i].out;
+		multi_or[12][i] = MultiOR(3);
+		multi_or[12][i].in[0] <== and[29][i].out;
+		multi_or[12][i].in[1] <== and[30][i].out;
+		multi_or[12][i].in[2] <== and[31][i].out;
+		states[i+1][10] <== multi_or[12][i].out;
+		from_zero_enabled[i] <== MultiNOR(10)([states_tmp[i+1][1], states[i+1][2], states[i+1][3], states[i+1][4], states[i+1][5], states[i+1][6], states[i+1][7], states[i+1][8], states[i+1][9], states[i+1][10]]);
+		states[i+1][1] <== MultiOR(2)([states_tmp[i+1][1], from_zero_enabled[i] * and[0][i].out]);
 		state_changed[i].in[0] <== states[i+1][1];
 		state_changed[i].in[1] <== states[i+1][2];
 		state_changed[i].in[2] <== states[i+1][3];
@@ -351,27 +382,29 @@ template Caret5Regex(msg_bytes) {
 		state_changed[i].in[5] <== states[i+1][6];
 		state_changed[i].in[6] <== states[i+1][7];
 		state_changed[i].in[7] <== states[i+1][8];
+		state_changed[i].in[8] <== states[i+1][9];
+		state_changed[i].in[9] <== states[i+1][10];
 	}
 
 	component final_state_result = MultiOR(num_bytes+1);
 	for (var i = 0; i <= num_bytes; i++) {
-		final_state_result.in[i] <== states[i][1];
+		final_state_result.in[i] <== states[i][10];
 	}
 	out <== final_state_result.out;
 	signal is_consecutive[msg_bytes+1][3];
 	is_consecutive[msg_bytes][2] <== 0;
 	for (var i = 0; i < msg_bytes; i++) {
-		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][1] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
+		is_consecutive[msg_bytes-1-i][0] <== states[num_bytes-i][10] * (1 - is_consecutive[msg_bytes-i][2]) + is_consecutive[msg_bytes-i][2];
 		is_consecutive[msg_bytes-1-i][1] <== state_changed[msg_bytes-i].out * is_consecutive[msg_bytes-1-i][0];
-		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][1], is_consecutive[msg_bytes-1-i][1]]);
+		is_consecutive[msg_bytes-1-i][2] <== ORAnd()([(1 - from_zero_enabled[msg_bytes-i+1]), states[num_bytes-i][10], is_consecutive[msg_bytes-1-i][1]]);
 	}
-	// substrings calculated: [{(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 1), (3, 2), (4, 2), (5, 2), (6, 4), (7, 4), (8, 4)}]
+	// substrings calculated: [{(2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (3, 10), (4, 3), (5, 3), (6, 3), (7, 5), (8, 5), (9, 5), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9), (10, 10)}]
 	signal is_substr0[msg_bytes];
 	signal is_reveal0[msg_bytes];
 	signal output reveal0[msg_bytes];
 	for (var i = 0; i < msg_bytes; i++) {
-		 // the 0-th substring transitions: [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 1), (3, 2), (4, 2), (5, 2), (6, 4), (7, 4), (8, 4)]
-		is_substr0[i] <== MultiOR(23)([states[i+1][0] * states[i+2][1], states[i+1][0] * states[i+2][2], states[i+1][0] * states[i+2][3], states[i+1][0] * states[i+2][4], states[i+1][0] * states[i+2][5], states[i+1][0] * states[i+2][6], states[i+1][0] * states[i+2][7], states[i+1][0] * states[i+2][8], states[i+1][1] * states[i+2][1], states[i+1][1] * states[i+2][2], states[i+1][1] * states[i+2][3], states[i+1][1] * states[i+2][4], states[i+1][1] * states[i+2][5], states[i+1][1] * states[i+2][6], states[i+1][1] * states[i+2][7], states[i+1][1] * states[i+2][8], states[i+1][2] * states[i+2][1], states[i+1][3] * states[i+2][2], states[i+1][4] * states[i+2][2], states[i+1][5] * states[i+2][2], states[i+1][6] * states[i+2][4], states[i+1][7] * states[i+2][4], states[i+1][8] * states[i+2][4]]);
+		 // the 0-th substring transitions: [(2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (3, 10), (4, 3), (5, 3), (6, 3), (7, 5), (8, 5), (9, 5), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9), (10, 10)]
+		is_substr0[i] <== MultiOR(23)([states[i+1][2] * states[i+2][3], states[i+1][2] * states[i+2][4], states[i+1][2] * states[i+2][5], states[i+1][2] * states[i+2][6], states[i+1][2] * states[i+2][7], states[i+1][2] * states[i+2][8], states[i+1][2] * states[i+2][9], states[i+1][2] * states[i+2][10], states[i+1][3] * states[i+2][10], states[i+1][4] * states[i+2][3], states[i+1][5] * states[i+2][3], states[i+1][6] * states[i+2][3], states[i+1][7] * states[i+2][5], states[i+1][8] * states[i+2][5], states[i+1][9] * states[i+2][5], states[i+1][10] * states[i+2][3], states[i+1][10] * states[i+2][4], states[i+1][10] * states[i+2][5], states[i+1][10] * states[i+2][6], states[i+1][10] * states[i+2][7], states[i+1][10] * states[i+2][8], states[i+1][10] * states[i+2][9], states[i+1][10] * states[i+2][10]]);
 		is_reveal0[i] <== is_substr0[i] * is_consecutive[i][2];
 		reveal0[i] <== in[i+1] * is_reveal0[i];
 	}
diff --git a/packages/compiler/src/lib.rs b/packages/compiler/src/lib.rs
index ebafd20..c6ba852 100644
--- a/packages/compiler/src/lib.rs
+++ b/packages/compiler/src/lib.rs
@@ -13,7 +13,7 @@ use crate::regex::*;
 use itertools::Itertools;
 use petgraph::prelude::*;
 use serde::{Deserialize, Serialize};
-use std::collections::{BTreeMap, BTreeSet};
+use std::collections::{BTreeMap, BTreeSet, VecDeque};
 use std::path::PathBuf;
 use thiserror::Error;
 
@@ -31,7 +31,7 @@ pub enum CompilerError {
 /// A configuration of decomposed regexes.
 #[derive(Debug, Clone, Serialize, Deserialize)]
 pub struct DecomposedRegexConfig {
-    pub parts: Vec<RegexPartConfig>,
+    pub parts: VecDeque<RegexPartConfig>,
 }
 
 /// Decomposed regex part.
@@ -64,7 +64,7 @@ pub struct DFAState {
 
 #[derive(Debug, Clone, Serialize, Deserialize)]
 pub struct DFAGraph {
-    states: Vec<DFAState>,
+    pub states: Vec<DFAState>,
 }
 
 #[derive(Debug, Clone, Serialize, Deserialize)]
@@ -89,7 +89,7 @@ pub struct SubstrsDefsJson {
 }
 
 impl DecomposedRegexConfig {
-    pub fn to_regex_and_dfa(&self) -> Result<RegexAndDFA, CompilerError> {
+    pub fn to_regex_and_dfa(&mut self) -> Result<RegexAndDFA, CompilerError> {
         Ok(regex_and_dfa(self))
     }
 }
@@ -127,7 +127,7 @@ pub fn gen_from_decomposed(
     circom_template_name: Option<&str>,
     gen_substrs: Option<bool>,
 ) {
-    let decomposed_regex_config: DecomposedRegexConfig =
+    let mut decomposed_regex_config: DecomposedRegexConfig =
         serde_json::from_reader(File::open(decomposed_regex_path).unwrap()).unwrap();
     let regex_and_dfa = decomposed_regex_config
         .to_regex_and_dfa()
diff --git a/packages/compiler/src/regex.rs b/packages/compiler/src/regex.rs
index 121feb7..2524fe0 100644
--- a/packages/compiler/src/regex.rs
+++ b/packages/compiler/src/regex.rs
@@ -1,4 +1,4 @@
-use crate::{DFAGraph, DFAState, DecomposedRegexConfig, RegexAndDFA, SubstrsDefs};
+use crate::{DFAGraph, DFAState, DecomposedRegexConfig, RegexAndDFA, RegexPartConfig, SubstrsDefs};
 use regex::Regex;
 use regex_automata::dfa::{dense::DFA, StartKind};
 use std::collections::{BTreeMap, BTreeSet};
@@ -252,7 +252,7 @@ fn add_dfa(net_dfa: &DFAGraph, graph: &DFAGraph) -> DFAGraph {
     net_dfa
 }
 
-pub fn regex_and_dfa(decomposed_regex: &DecomposedRegexConfig) -> RegexAndDFA {
+pub fn regex_and_dfa(decomposed_regex: &mut DecomposedRegexConfig) -> RegexAndDFA {
     let mut config = DFA::config().minimize(true);
     config = config.start_kind(StartKind::Anchored);
     config = config.byte_classes(false);
@@ -260,17 +260,87 @@ pub fn regex_and_dfa(decomposed_regex: &DecomposedRegexConfig) -> RegexAndDFA {
 
     let mut net_dfa = DFAGraph { states: Vec::new() };
     let mut substr_defs_array = Vec::new();
+    
+    let caret_regex_index = {
+        let first_regex = decomposed_regex.parts[0].regex_def.as_bytes();
+        let mut is_in_parenthesis = false;
+        let mut caret_found = false;
+        let mut idx = 0;
+        while idx < first_regex.len() {
+            let byte = first_regex[idx];
+            if byte == b'\\' {
+                idx += 2;
+            } else if byte == b'(' {
+                is_in_parenthesis = true;
+                idx += 1;
+            } else if byte == b'[' {
+                idx += 2;
+            } else if byte == b')' {
+                debug_assert!(is_in_parenthesis, "Unmatched parenthesis");
+                is_in_parenthesis = false;
+                idx += 1;
+                if caret_found {
+                    break;
+                }
+            } else if byte == b'^' {
+                caret_found = true;
+                idx += 1;
+                if !is_in_parenthesis {
+                    break;
+                }
+            } else {
+                idx += 1;
+            }
+        }
 
-    for regex in decomposed_regex.parts.iter() {
-        let regex_str = regex.regex_def.as_str();
-        println!("{:?}", regex_str);
+        if caret_found {
+            Some(idx)
+        } else {
+            None
+        }
+    };
+    if let Some(index) = caret_regex_index {
+        let caret_regex = decomposed_regex.parts[0].regex_def[0..index].to_string();
+        decomposed_regex.parts.push_front(RegexPartConfig {
+            is_public: false,
+            regex_def: caret_regex,
+        });
+        decomposed_regex.parts[1].regex_def = decomposed_regex.parts[1].regex_def[index..].to_string();
+    }
+
+    for (idx, regex) in decomposed_regex.parts.iter().enumerate() {
         let re = DFA::builder()
             .configure(config.clone())
-            .build(&format!(r"^{}$", regex_str))
+            .build(&format!(r"^{}$", regex.regex_def.as_str()))
             .unwrap();
         let re_str = format!("{:?}", re);
         let mut graph = dfa_to_graph(&parse_dfa_output(&re_str));
-        println!("{:?}", graph);
+        if idx == 0 && caret_regex_index.is_some() {
+            if regex.regex_def.as_str() == "^" {
+                graph = DFAGraph {
+                    states: vec![
+                        DFAState {
+                            r#type: "".to_string(),
+                            edges: BTreeMap::from([(1, BTreeSet::from([255u8]))]),
+                            state: 0,
+                        },
+                        DFAState {
+                            r#type: "accept".to_string(),
+                            edges: BTreeMap::new(),
+                            state: 1,
+                        }
+                    ],
+                }
+            } else {
+                if let Some(edge) = graph.states[0].edges.get_mut(&1) {
+                    edge.insert(255u8);
+                } else {
+                    graph.states[0].edges.insert(1, BTreeSet::from([255u8]));
+                }
+                graph.states[0].r#type = "".to_string();
+            }
+        }
+        // println!("{:?}", graph);
         // Find max state in net_dfa
         let mut max_state_index = 0;
         for state in net_dfa.states.iter() {
@@ -324,7 +394,7 @@ pub fn regex_and_dfa(decomposed_regex: &DecomposedRegexConfig) -> RegexAndDFA {
 
         net_dfa = add_dfa(&net_dfa, &graph);
     }
-    println!("{:?}", net_dfa);
+    // println!("{:?}", net_dfa);
 
     let mut regex_str = String::new();
     for regex in decomposed_regex.parts.iter() {
diff --git a/packages/compiler/src/wasm.rs b/packages/compiler/src/wasm.rs
index ce79661..5099f68 100644
--- a/packages/compiler/src/wasm.rs
+++ b/packages/compiler/src/wasm.rs
@@ -5,7 +5,7 @@ use wasm_bindgen::prelude::*;
 #[wasm_bindgen]
 #[allow(non_snake_case)]
 pub fn genFromDecomposed(decomposedRegexJson: &str, circomTemplateName: &str) -> String {
-    let decomposed_regex_config: DecomposedRegexConfig =
+    let mut decomposed_regex_config: DecomposedRegexConfig =
         serde_json::from_str(decomposedRegexJson).expect("failed to parse decomposed_regex json");
     let regex_and_dfa = decomposed_regex_config
         .to_regex_and_dfa()
@@ -30,8 +30,8 @@ pub fn genFromRaw(rawRegex: &str, substrsJson: &str, circomTemplateName: &str) -
 #[wasm_bindgen]
 #[allow(non_snake_case)]
 pub fn genRegexAndDfa(decomposedRegex: JsValue) -> JsValue {
-    let decomposed_regex_config: DecomposedRegexConfig = from_value(decomposedRegex).unwrap();
-    let regex_and_dfa = regex_and_dfa(&decomposed_regex_config);
+    let mut decomposed_regex_config: DecomposedRegexConfig = from_value(decomposedRegex).unwrap();
+    let regex_and_dfa = regex_and_dfa(&mut decomposed_regex_config);
     let dfa_val_str = serde_json::to_string(&regex_and_dfa).unwrap();
     JsValue::from_str(&dfa_val_str)
 }
@@ -39,8 +39,8 @@ pub fn genRegexAndDfa(decomposedRegex: JsValue) -> JsValue {
 #[wasm_bindgen]
 #[allow(non_snake_case)]
 pub fn genCircom(decomposedRegex: JsValue, circomTemplateName: &str) -> String {
-    let decomposed_regex_config: DecomposedRegexConfig = from_value(decomposedRegex).unwrap();
-    let regex_and_dfa = regex_and_dfa(&decomposed_regex_config);
+    let mut decomposed_regex_config: DecomposedRegexConfig = from_value(decomposedRegex).unwrap();
+    let regex_and_dfa = regex_and_dfa(&mut decomposed_regex_config);
     regex_and_dfa
         .gen_circom_str(&circomTemplateName)
         .expect("failed to generate circom")