diff --git a/src/sage/combinat/words/automataC.c b/src/sage/combinat/words/automataC.c
index 123ba900501..7bb1b1982b3 100644
--- a/src/sage/combinat/words/automataC.c
+++ b/src/sage/combinat/words/automataC.c
@@ -98,9 +98,9 @@ Automaton NewAutomaton (int n, int na)
 	Automaton a;
 	a.n = n;
 	a.na = na;
+	a.i = -1;
 	if (n == 0)
 	{
-		a.i = -1;
 		a.e = NULL;
 		return a;
 	}
@@ -111,7 +111,7 @@ Automaton NewAutomaton (int n, int na)
 		printf("Out of memory !");
 		exit(6);
 	}
-	int i;
+	int i,j;
 	for (i=0;i<n;i++)
 	{
 		a.e[i].f = (int *)malloc(sizeof(int)*na);
@@ -120,6 +120,10 @@ Automaton NewAutomaton (int n, int na)
 			printf("Out of memory !");
 			exit(7);
 		}
+		for (j=0;j<na;j++)
+		{
+			a.e[i].f[j] = -1;
+		}
 	}
 	return a;
 }
@@ -1432,6 +1436,33 @@ Automaton Determinise (Automaton a, Dict d, bool noempty, bool onlyfinals, bool
 {
 	int i;
 	
+	Automaton r;
+	if (a.i == -1)
+	{
+		//calcule la taille de l'alphabet
+		int nv = 0;
+		for (i=0;i<d.n;i++)
+		{
+			if (d.e[i] >= nv)
+				nv = d.e[i]+1;
+		}
+		//
+		if (verb)
+			printf("Pas d'état initial !\n");
+		if (nof)
+		{
+			r = NewAutomaton(1, nv);
+			r.i = 0;
+			r.e[0].final = true;
+			for (i=0;i<nv;i++)
+			{
+				r.e[0].f[i] = 0;
+			}
+		}else
+			r = NewAutomaton(0, nv);
+		return r;
+	}
+	
 	//increase the stack size
 	const rlim_t kStackSize = 32 * 1024 * 1024;
 	struct rlimit rl;
@@ -1493,24 +1524,6 @@ Automaton Determinise (Automaton a, Dict d, bool noempty, bool onlyfinals, bool
 	//initialise l'automate résultat avec juste l'état initial
 	if (verb)
 		printf("Init r...\n");
-	Automaton r;
-	if (a.i == -1)
-	{
-		if (verb)
-			printf("Pas d'état initial !\n");
-		if (nof)
-		{
-			r = NewAutomaton(1, id.n);
-			r.i = 0;
-			r.e[0].final = true;
-			for (i=0;i<id.n;i++)
-			{
-				r.e[0].f[i] = 0;
-			}
-		}else
-			r = NewAutomaton(0, id.n);
-		return r;
-	}
 	r.n = 1;
 	r.na = id.n;
 	r.i = 0;
diff --git a/src/sage/combinat/words/cautomata.pyx b/src/sage/combinat/words/cautomata.pyx
index 575fa8f4e05..ae33f047470 100644
--- a/src/sage/combinat/words/cautomata.pyx
+++ b/src/sage/combinat/words/cautomata.pyx
@@ -1067,7 +1067,17 @@ cdef class FastAutomaton:
 		sig_on()
 		AddEtat(self.a, final)
 		sig_off()
-
+		return self.a.n-1
+	
+	def add_edge (self, int i, l, int j):
+		if i >= self.a.n: raise ValueError("L'etat %s n'existe pas."%i)
+		if j >= self.a.n: raise ValueError("L'etat %s n'existe pas."%j)
+		try:
+			k = self.A.index(l)
+		except:
+			raise ValueError("La lettre %s n'existe pas."%l)
+		self.a.e[i].f[k] = j
+		
 	def n_states (self):
 		return self.a.n
 
diff --git a/src/sage/monoids/beta_adic_monoid.pyx b/src/sage/monoids/beta_adic_monoid.pyx
index f7848368f9b..c810e7aaaa6 100644
--- a/src/sage/monoids/beta_adic_monoid.pyx
+++ b/src/sage/monoids/beta_adic_monoid.pyx
@@ -1514,6 +1514,13 @@ class BetaAdicMonoid(Monoid_class):
 			Cd is the set of differences A-B where A and B are the alphabets to compare.
 			t is the translation of one of the side (initial state of the automaton).
 			ext : automate des relations à l'infini ou pas.
+			
+			
+		TESTS::
+		
+			sage: pi = x^3-x^2-x-1
+			sage: b = pi.roots(ring=QQbar)[1][0]
+			sage: m = BetaAdicMonoid(b, [0,1]).relations_automaton3()		
 		"""
 		if Cd is None:
 			Cd = Set([c-c2 for c in self.C for c2 in self.C])
@@ -2626,16 +2633,21 @@ class BetaAdicMonoid(Monoid_class):
 		#compute the relations automaton with translation t
 		ar = self.relations_automaton4(t=t, A=A, B=B, couples=True, verb=verb)
 		#compute the product of a and b
+		if verb: print("product...")
 		ap = a.product(b)
 		#compute the intersections
+		if verb: print("intersection...")
 		ai = ar.intersection(ap)
+		if verb: print("min...")
 		ai = ai.minimise()
 		#project on one side
 		d={}
 		for c1 in A:
 			for c2 in B:
 				d[(c1,c2)] = c2
+		if verb: print("determinise...")
 		ai = ai.determinise_proj(d, verb=verb)
+		if verb: print("min")
 		return ai.minimise()
 	
 	#Not well tested !!!!
diff --git a/src/sage/monoids/relations.c b/src/sage/monoids/relations.c
index aefc8c781a4..902f55b7ca3 100644
--- a/src/sage/monoids/relations.c
+++ b/src/sage/monoids/relations.c
@@ -22,7 +22,7 @@ Automate NewAutomaton (int n, int na)
 		printf("Out of memory !");
 		exit(6);
 	}
-	int i;
+	int i, j;
 	for (i=0;i<n;i++)
 	{
 		a.e[i].f = (int *)malloc(sizeof(int)*na);
@@ -31,6 +31,10 @@ Automate NewAutomaton (int n, int na)
 			printf("Out of memory !");
 			exit(7);
 		}
+		for (j=0;j<na;j++)
+		{
+			a.e[i].f[j] = -1;
+		}
 	}
 	return a;
 }
@@ -49,8 +53,9 @@ InfoBetaAdic iba; //variable globale contenant les infos sur le développement e
 
 Element NewElement (int n)
 {
+	//printf("NewElement(%d)\n", n);
 	Element e;
-	e.c = (int*)malloc(sizeof(int)*n);
+	e.c = (coeff *)malloc(sizeof(coeff)*n);
 	return e;
 }
 
@@ -101,15 +106,27 @@ void initHash ()
 	int i;
 	for (i=0;i<nhash;i++)
 	{
-		thash[i].e = NULL;
+		//thash[i].e = NULL;
 		thash[i].n = 0;
 	}
 }
 
 void freeInfoBetaAdic (InfoBetaAdic iba)
 {
-	int i;
+	int i,j;
 	free(pile);
+	for (i=0;i<nhash;i++)
+	{
+		for (j=0;j<thash[i].n;j++)
+		{
+			FreeElement(thash[i].e[j]);
+		}
+		if (thash[i].n)
+		{
+			free(thash[i].e);
+			free(thash[i].ind);
+		}
+	}
 	free(thash);
 	free(iba.cM);
 	for (i=0;i<iba.ncmax;i++)
@@ -295,9 +312,17 @@ bool inHash (Element e)
 		}
 	}
 	//ajoute l'élément
-	thash[h].e = (Element *)realloc(thash[h].e, thash[h].n+1);
-	//thash[h].ne = (int *)realloc(thash[h].ne, thash[h].n+1);
-	thash[h].ind = (int *)realloc(thash[h].ind, thash[h].n+1);
+	if (thash[h].n)
+	{
+		thash[h].e = (Element *)realloc(thash[h].e, sizeof(Element)*(thash[h].n+1));
+		//thash[h].ne = (int *)realloc(thash[h].ne, thash[h].n+1);
+		thash[h].ind = (int *)realloc(thash[h].ind, sizeof(int)*(thash[h].n+1));
+	}else
+	{
+		thash[h].e = (Element *)malloc(sizeof(Element));
+		//thash[h].ne = (int *)realloc(thash[h].ne, thash[h].n+1);
+		thash[h].ind = (int *)malloc(sizeof(int));
+	}
 	if (!thash[h].e || !thash[h].ind)
 	{
 		printf("Out of memory !!!\n");
@@ -487,6 +512,12 @@ Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool ext, bool verb
 		{
 			FreeElement(thash[i].e[j]);
 		}
+		if (thash[i].n)
+		{
+			free(thash[i].e);
+			free(thash[i].ind);
+		}
+		thash[i].n = 0;
 	}
 	FreeElement(s);
 	FreeElement(e);
@@ -584,9 +615,9 @@ Automate RelationsAutomatonT (InfoBetaAdic iba2, Element t, bool isvide, bool ex
 					pile[n] = NewElement(iba.n);
 					copy(s, pile[n]);
 					n++;
-					if (n > npile)
+					if (n >= npile)
 					{
-						printf("Erreur : dépassement de la pile !!!\n");
+						printf("*****************************************\n*** Erreur : dépassement de la pile !!! ***\n*****************************************\n");
 					}
 				}else
 				{//on retombe sur un état déjà vu
@@ -612,13 +643,6 @@ Automate RelationsAutomatonT (InfoBetaAdic iba2, Element t, bool isvide, bool ex
 	
 	//créé l'automate
 	Automate r = NewAutomaton(compteur, iba.nc);
-	for (i=0;i<r.n;i++)
-	{
-		for (j=0;j<r.na;j++)
-		{
-			r.e[i].f[j] = -1;
-		}
-	}
 	int k, ind;
 	for (i=0;i<nhash;i++)
 	{
@@ -667,6 +691,12 @@ Automate RelationsAutomatonT (InfoBetaAdic iba2, Element t, bool isvide, bool ex
 		{
 			FreeElement(thash[i].e[j]);
 		}
+		if (thash[i].n)
+		{
+			free(thash[i].e);
+			free(thash[i].ind);
+		}
+		thash[i].n = 0;
 	}
 	FreeElement(s);
 	FreeElement(e);
diff --git a/src/sage/monoids/relations.h b/src/sage/monoids/relations.h
index 872c122ad0d..c00a5512692 100644
--- a/src/sage/monoids/relations.h
+++ b/src/sage/monoids/relations.h
@@ -1,13 +1,15 @@
 
+typedef long int coeff;
+
 struct Element
 {
-	long int *c; //liste des n coeffs
+	coeff *c; //liste des n coeffs
 };
 typedef struct Element Element;
 
 struct PlaceArch
 {
-	Complexe *c; //1, b, b^2, ... pour cette place
+	Complexe *c; //1, b, b^2, ..., b^(n-1) pour cette place
 };
 typedef struct PlaceArch PlaceArch;