Add functions rec_word() and find_word() to FastAutomaton, and modify…

… function is_empty().

src/sage/combinat/words/automataC.c

@@ -739,6 +739,54 @@ bool emptyLangage (Automaton a)
 	return res;
 }
 
+bool findWord_rec (Automaton a, int e, int n, Dict *w, bool verb)
+{
+	if (a.e[e].final)
+	{
+		if (verb)
+			printf("Alloue un mot de taille %d.\n", n);
+		*w = NewDict(n);
+		return true;
+	}
+	//indique que le sommet a été vu
+	a.e[e].final |= 2;
+	//parcours les fils
+	int i;
+	for (i=0;i<a.na;i++)
+	{
+		if (a.e[e].f[i] != -1)
+		{
+			if (a.e[a.e[e].f[i]].final & 2)
+				continue; //ce fils a déjà été vu
+			if (findWord_rec(a, a.e[e].f[i], n+1, w, verb))
+			{
+				if (verb)
+				{
+					printf("w[%d] = %d\n", n, i);
+				}
+				w->e[n] = i;
+				return true;
+			}
+		}
+	}
+	return false;
+}
+
+//rend un mot dans le langage de a
+bool findWord (Automaton a, Dict *w, bool verb)
+{
+	if (a.i == -1)
+		return false;
+	bool res = findWord_rec(a, a.i, 0, w, verb);
+	//remet les états finaux
+	int i;
+	for (i=0;i<a.n;i++)
+	{
+		a.e[i].final &= 1;
+	}
+	return res;
+}
+
 inline int contract (int i1, int i2, int n1)
 {
 	return i1+n1*i2;

src/sage/combinat/words/automataC.h

@@ -13,6 +13,8 @@ struct Dict
 };
 typedef struct Dict Dict;
 
+bool findWord (Automaton a, Dict *w, bool verb); //rend un mot dans le langage de a
+
 Dict NewDict (int n);
 void FreeDict (Dict d);
 void printDict (Dict d);

src/sage/combinat/words/cautomata.pyx

@@ -79,6 +79,7 @@ cdef extern from "automataC.h":
 	bool IsCompleteAutomaton (Automaton a)
 	bool CompleteAutomaton (Automaton *a)
 	Automaton BiggerAlphabet (Automaton a, Dict d, int nna) #copy the automaton with a new bigger alphabet
+	bool findWord (Automaton a, Dict *w, bool verb)
 	void Test ()
 
 #dictionnaire numérotant l'alphabet projeté
@@ -1070,6 +1071,33 @@ cdef class FastAutomaton:
 		res = equalsLangages(self.a, a2.a, d, minimized)
 		sig_off()
 		return Bool(res)
+
+	def find_word (self, bool verb=False):
+		sig_on()
+		cdef Dict w
+		res = findWord (self.a[0], &w, verb)
+		sig_off()
+		if not res:
+			return None
+		r = []
+		for i in range(w.n):
+			r.append(self.A[w.e[i]])
+		FreeDict(w)
+		return r
+
+	#determine if the word is recognized by the automaton or not
+	def rec_word (self, list w):
+		cdef int e = self.a.i
+		if e == -1:
+			return False
+		d = {}
+		for i,a in enumerate(self.A):
+			d[a] = i
+		for a in w:
+			e = self.a.e[e].f[d[a]]
+			if e == -1:
+				return False
+		return Bool(self.a.e[e].final)
 
 	def add_state (self, bool final):
 		sig_on()
@@ -1154,14 +1182,15 @@ cdef class FastAutomaton:
 
 	#tell if the language of the automaton is empty
 	#(this function is not very efficient)
-	def is_empty (self, ext=True):
-		if ext:
-			return self.emonde().emonde_inf().n_states() == 0
-		else:
-			return self.emonde().n_states() == 0
+	def is_empty (self, ext=False):
+		return (self.find_word() is None)
+		#if ext:
+		#	return self.emonde().emonde_inf().n_states() == 0
+		#else:
+		#	return self.emonde().n_states() == 0
 
 	#determine if the languages intersect
-	def intersect (self, FastAutomaton b, ext=True):
+	def intersect (self, FastAutomaton b, ext=False):
 		return not self.intersection(b).is_empty(ext)
 
 	def random_word (self, int nmin=-1, int nmax=100):