Reachability in Parameterized Systems: All Flavors of Threshold Automata

Authors Jure Kukovec, Igor Konnov , Josef Widder

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Jure Kukovec
  • TU Wien, Favoritenstraße 9 - 11, 1040 Vienna, Austria
Igor Konnov
  • University of Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Josef Widder
  • TU Wien, Favoritenstraße 9 - 11, 1040 Vienna, Austria

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Jure Kukovec, Igor Konnov, and Josef Widder. Reachability in Parameterized Systems: All Flavors of Threshold Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Threshold automata, and the counter systems they define, were introduced as a framework for parameterized model checking of fault-tolerant distributed algorithms. This application domain suggested natural constraints on the automata structure, and a specific form of acceleration, called single-rule acceleration: consecutive occurrences of the same automaton rule are executed as a single transition in the counter system. These accelerated systems have bounded diameter, and can be verified in a complete manner with bounded model checking. We go beyond the original domain, and investigate extensions of threshold automata: non-linear guards, increments and decrements of shared variables, increments of shared variables within loops, etc., and show that the bounded diameter property holds for several extensions. Finally, we put single-rule acceleration in the scope of flat counter automata: although increments in loops may break the bounded diameter property, the corresponding counter automaton is flattable, and reachability can be verified using more permissive forms of acceleration.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Software verification
  • Theory of computation → Logic and verification
  • Software and its engineering → Software fault tolerance
  • threshold & counter automata
  • parameterized verification
  • reachability


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