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What's Decidable about Availability Languages?

Authors Parosh Aziz Abdulla, Mohamed Faouzi Atig, Roland Meyer, Mehdi Seyed Salehi

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Parosh Aziz Abdulla
Mohamed Faouzi Atig
Roland Meyer
Mehdi Seyed Salehi

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Parosh Aziz Abdulla, Mohamed Faouzi Atig, Roland Meyer, and Mehdi Seyed Salehi. What's Decidable about Availability Languages?. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 192-205, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.FSTTCS.2015.192

Abstract

We study here the algorithmic analysis of systems modeled in terms of availability languages. Our first main result is a positive answer to the emptiness problem: it is decidable whether a given availability language contains a word. The key idea is an inductive construction that replaces availability languages with Parikh-equivalent regular languages. As a second contribution, we solve the intersection problem modulo bounded languages: given availability languages and a bounded language, it is decidable whether the intersection of the former contains a word from the bounded language. We show that the problem is NP-complete. The idea is to reduce to satisfiability of existential Presburger arithmetic. Since the (general) intersection problem for availability languages is known to be undecidable, our results characterize the decidability border for this model.  Our last contribution is a study of the containment problem between regular and availability languages. We show that safety verification, i.e., checking containment of an availability language in a regular language, is decidable. The containment problem of regular languages in availability languages is proven undecidable.

Subject Classification

Keywords
  • Availability
  • formal languages
  • emptiness
  • decidability

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