Conjugacy and Equivalence of Weighted Automata and Functional Transducers

We show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) field and that the same holds true for functional tranducers as well. abstract 1 Presentation of the results In a recent paper ([1]), we have studied the equivalence of Z-automata. This equivalence is known to be decidable (with polynomial complexity) for more than forty years but we showed there two results that give more structural information on two equivalent Z-automata. We first proved that two equivalent Z-automata are related by a series of three conjugacies -- we shall define conjugacy later in the paper -- and then that every conjugacy relation can be decomposed into a sequence of three operations: state (out-)splitting (also known as covering), circulation of coefficients, and state (in-)merging (also known as co-covering). Altogether, we reached a decomposition of any equivalence between Z-automata as the one described at Figure 1 [Conjugacy is represented by double...

• Type: Conference
• Year: 2006
• Where: CSR
• Authors: Marie-Pierre Béal, Sylvain Lombardy, Jacques Sakarovitch
• Keywords: CSR 2006, Equivalent K-automata, Equivalent Z-automata, Simple Solid Arrows, Theoretical Computer Science