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What's decidable about availability languages?

Abdulla, P. A ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.4230/LIPIcs.FSTTCS.2015.192
  3. Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2015
  4. Abstract:
  5. 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
  6. Keywords:
  7. Decidability ; Emptiness ; Formal languages ; Algorithmic languages ; Algorithms ; Availability ; Computability and decidability ; Context free languages ; Digital arithmetic ; Formal languages ; Problem solving ; Software engineering ; Algorithmic analysis ; Bounded language ; Emptiness ; Emptiness problem ; Inductive Construction ; Intersection problem ; Presburger arithmetic ; Safety verification ; Computational linguistics
  8. Source: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015, 16 December 2015 through 18 December 2015 ; Volume 45 , 2015 , Pages 192-205 ; 18688969 (ISSN) ; 9783939897972 (ISBN)
  9. URL: http://drops.dagstuhl.de/opus/volltexte/2015/5660