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Bounded Reachability Problems Are Decidable in FIFO Machines

Authors Benedikt Bollig, Alain Finkel, Amrita Suresh

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Benedikt Bollig
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France
Alain Finkel
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France
Amrita Suresh
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France

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Benedikt Bollig, Alain Finkel, and Amrita Suresh. Bounded Reachability Problems Are Decidable in FIFO Machines. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 49:1-49:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CONCUR.2020.49

Abstract

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are input-bounded (i.e. the sequence of messages sent through a particular channel belongs to a given bounded language). We prove, by reducing this model to a counter machine with restricted zero tests, that the rational-reachability problem (and by extension, control-state reachability, unboundedness, deadlock, etc.) is decidable. This class of machines subsumes input-letter-bounded machines, flat machines, linear FIFO nets, and monogeneous machines, for which some of these problems were already shown to be decidable. These theoretical results can form the foundations to build a tool to verify general FIFO machines based on the analysis of input-bounded machines.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • FIFO machines
  • reachability
  • underapproximation
  • counter machines

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