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Communication Dans Un Congrès Année : 2019

The Quantifier Alternation Hierarchy of Synchronous Relations

Résumé

The class of synchronous relations, also known as automatic or regular, is one of the most studied subclasses of rational relations. It enjoys many desirable closure properties and is known to be logically characterized: the synchronous relations are exactly those that are defined by a first-order formula on the structure of all finite words, with the prefix, equal-length and last-letter predicates. Here, we study the quantifier alternation hierarchy of this logic. We show that it collapses at level \Sigma_3 and that all levels below admit decidable characterizations. Our results reveal the connections between this hierarchy and the well-known hierarchy of first-order defined languages of finite words.
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Dates et versions

hal-02109188 , version 1 (24-04-2019)
hal-02109188 , version 2 (27-06-2019)
hal-02109188 , version 3 (22-09-2020)

Identifiants

Citer

Diego Figueira, Varun Ramanathan, Pascal Weil. The Quantifier Alternation Hierarchy of Synchronous Relations. International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2019, Aachen, Germany. pp.29:1-29:14, ⟨10.4230/LIPIcs.MFCS.2019.29⟩. ⟨hal-02109188v3⟩
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