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Checking Presence Reachability Properties on Parameterized Shared-Memory Systems

Author Nicolas Waldburger

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Nicolas Waldburger
  • Univ Rennes, Inria, CNRS, IRISA, France


Many thanks to Nathalie Bertrand, Nicolas Markey and Ocan Sankur for their invaluable advice.

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Nicolas Waldburger. Checking Presence Reachability Properties on Parameterized Shared-Memory Systems. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 88:1-88:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the standard model with finitely many registers, we tackle round-based shared-memory systems with fresh registers at each round. In the latter model, both the number of processes and the number of registers are unbounded, making verification particularly challenging. The properties studied are generic presence reachability objectives, which subsume classical questions such as safety or synchronization by expressing the presence or absence of processes in some states. In the more general round-based setting, we establish that the parameterized verification of presence reachability properties is PSPACE-complete. Moreover, for the roundless model with finitely many registers, we prove that the complexity drops down to NP-complete and we provide several natural restrictions that make the problem solvable in polynomial time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Verification by model checking
  • Theory of computation → Distributed algorithms
  • Verification
  • Parameterized models
  • Distributed algorithms


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