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Communication Dans Un Congrès Année : 2017

Regular Separability of Parikh Automata

Résumé

We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model, we surprisingly show decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is disjoint from the other? We supplement this result by proving undecidability of the same problem already for languages of visibly one counter automata. We investigate separability problems for languages of finite words. We say that a language U is separated from a language V by S if U ⊆ S and V ∩ S = ∅. In the sequel we also often say that U and V are separated by S. For two families of languages F and G, the F separability problem for G asks for two given languages U, V ∈ G whether U is separated from V by some language from F. The same notion of separability makes clearly sense if F and G are classes of sets of vectors instead of classes of languages. In this paper, we consider the case where F are regular languages and G languages recognized by Parikh automata, and the case where F are the unary sets and G the semilinear sets. Motivation. Separability is a classical problem in theoretical computer science. It was investigated most extensively in the area of formal languages, for G being the family of all regular word languages. Since regular languages are effectively closed under complement, the
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Dates et versions

hal-01587616 , version 1 (14-09-2017)

Identifiants

Citer

Lorenzo Clemente, Wojciech Czerwiński, Sławomir Lasota, Charles Paperman. Regular Separability of Parikh Automata. The 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)), 2017, Varsovie, Poland. ⟨10.4230/LIPIcs.ICALP.2017.117⟩. ⟨hal-01587616⟩
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