Géraud Sénizergues

L(A) = L(B) ? decidability results from complete formal systems

Abstract The equivalence problem for deterministic pushdown automata is shown to be decidable. We exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda M . We then extend the result to deterministic pushdown transducers from a free monoid into an abelian group. A general algebraic and logical framework, inspired by Harrison et al. (Theoret. Comput. Sci. 9 (1979) 173–205), Conrcelle (Theoret. Comput. Sci. 6 (1978) 255–279) and Meitus (Kybernetika 5 (1989) 14–25 (in Russian)) is developed.

The Equivalence Problem for Deterministic Pushdown Automata is Decidable

The equivalence problem for deterministic pushdown automata is shown to be decidable. We exhibit a complete formal system for deducing equivalent pairs of deterministic rational series on the alphabet associated with a dpda M.

Decidability of bisimulation equivalence for equational graphs of finite out-degree

The bisimulation problem for equational graphs of finite out-degree is shown to be decidable. We reduce this problem to the /spl eta/-bisimulation problem for deterministic rational (vectors of) Boolean series on the alphabet of a dpda M. We then exhibit a complete formal system for deducing equivalent pairs of such vectors.

The Bisimulation Problem for Equational Graphs of Finite Out-Degree

The bisimulation problem for equational graphs of finite out-degree is shown to be decidable. We reduce this problem to the

Groups and NTS languages

\eta

L(A)=L(B)? a simplified decidability proof

-bisimulation problem for deterministic rational (vectors of) boolean series on the alphabet of a deterministic pushdown automaton

On the Termination Problem for One-Rule Semi-Thue System

{\cal M}

Some decision problems about controlled rewriting systems

. We then exhibit a complete formal system for deducing equivalent pairs of such vectors.

Bottom-up rewriting is inverse recognizability preserving

Abstract The context-free groups are known to be exactly the finitely generated virtually free groups [19, 11]. We give here a new combinatorial property which characterizes these groups: they are “locally primary.” A corollary of this property is that the cylinder generated by the group languages is included in the family of NTS languages. In particular, every context-free group language is NTS.

The equivalence problem for t-turn dpda is co-NP

We give a proof of decidability of the equivalence problem for deterministic pushdown automata, which simplifies that of Senizergues (Theoret. Comput. Sci. 251 (2000) 1).