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Communication Dans Un Congrès Année : 2014

ACME: Automata with Counters, Monoids and Equivalence

Résumé

We present ACME, a tool implementing algebraic techniques to solve decision problems from automata theory. The core generic algorithm takes as input an automaton and computes its stabilization monoid, which is a generalization of its transition monoid. Using the stabilization monoid, one can solve many problems: determine whether a B-automaton (which is a special kind of automata with counters) is limited, whether two B-automata are equivalent, and whether a probabilistic leaktight automaton has value 1. The dedicated webpage where the tool ACME can be downloaded is The notion of stabilization monoids appears in two distinct contexts. It has first been developed in the theory of regular cost functions, introduced by Colcom-bet [Col09,Col13]. The underlying ideas have then been transferred to the setting of probabilistic automata [FGO12]. 1.1 Stabilization Monoids in the Theory of Regular Cost Functions At the heart of the theory of regular cost functions lies the equivalence between different formalisms: a logical formalism, cost MSO, two automata model, Band S-automata, and an algebraic counterpart, stabilization monoids. Here we briefly describe the model of B-automata, and their transformations to stabilization monoid. This automaton model generalizes the non-deterministic automata by adding a finite set of counters. Instead of accepting or rejecting a word as a non-deterministic automaton does, a B-automaton associates an The research leading to these results has received funding from the French ANR project 2010 BLAN 0202 02 FREC, the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement 259454 (GALE) and 239850 (SOSNA).
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Dates et versions

hal-02101510 , version 1 (16-04-2019)

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Nathanaël Fijalkow, Denis Kuperberg. ACME: Automata with Counters, Monoids and Equivalence. ATVA, 2014, Sydney, Australia. pp.163-167, ⟨10.1007/978-3-319-11936-6_12⟩. ⟨hal-02101510⟩

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