Regular Separability of Well-Structured Transition Systems

Authors Wojciech Czerwinski , Slawomir Lasota , Roland Meyer , Sebastian Muskalla , K. Narayan Kumar, Prakash Saivasan

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Wojciech Czerwinski
  • University of Warsaw, Poland
Slawomir Lasota
  • University of Warsaw, Poland
Roland Meyer
  • TU Braunschweig, Germany
Sebastian Muskalla
  • TU Braunschweig, Germany
K. Narayan Kumar
  • Chennai Mathematical Institute and UMI RELAX, India
Prakash Saivasan
  • TU Braunschweig, Germany

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Wojciech Czerwinski, Slawomir Lasota, Roland Meyer, Sebastian Muskalla, K. Narayan Kumar, and Prakash Saivasan. Regular Separability of Well-Structured Transition Systems. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We investigate the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that, under very mild assumptions, every two disjoint WSTS languages are regular separable: There is a regular language containing one of them and being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. In particular, no subclass of WSTS languages beyond the regular languages is closed under complement. Our second result shows that for Petri nets, the complexity of the backwards coverability algorithm yields a bound on the size of the regular separator. We complement it by a lower bound construction.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Regular languages
  • Theory of computation → Parallel computing models
  • regular separability
  • wsts
  • coverability languages
  • Petri nets


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