Unboundedness Problems for Languages of Vector Addition Systems

Authors Wojciech Czerwinski , Piotr Hofman , Georg Zetzsche

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Wojciech Czerwinski
  • University of Warsaw, Poland
Piotr Hofman
  • University of Warsaw, Poland
Georg Zetzsche
  • IRIF (Université Paris-Diderot & CNRS), France

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Wojciech Czerwinski, Piotr Hofman, and Georg Zetzsche. Unboundedness Problems for Languages of Vector Addition Systems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 119:1-119:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision procedures for such languages. This is especially true for checking properties that state the existence of infinitely many words of a particular shape. Informally, we call these unboundedness properties. We present a simple set of axioms for predicates that can express unboundedness properties. Our main result is that such a predicate is decidable for VAS languages as soon as it is decidable for regular languages. Among other results, this allows us to show decidability of (i) separability by bounded regular languages, (ii) unboundedness of occurring factors from a language K with mild conditions on K, and (iii) universality of the set of factors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Formal languages and automata theory
  • vector addition systems
  • decision problems
  • unboundedness
  • separability


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