Model checking parameterized asynchronous shared-memory systems
- 204 Downloads
We characterize the complexity of liveness verification for parameterized systems consisting of a leader process and arbitrarily many anonymous and identical contributor processes. Processes communicate through a shared, bounded-value register. While each operation on the register is atomic, there is no synchronization primitive to execute a sequence of operations atomically. We analyze the case in which processes are modeled by finite-state machines or pushdown machines and the property is given by a Büchi automaton over the alphabet of read and write actions of the leader. We show that the problem is decidable, and has a surprisingly low complexity: it is NP-complete when all processes are finite-state machines, and is in NEXPTIME (and PSPACE-hard) when they are pushdown machines. This complexity is lower than for the non-parameterized case: liveness verification of finitely many finite-state machines is PSPACE-complete, and undecidable for two pushdown machines. For finite-state machines, our proofs characterize infinite behaviors using existential abstraction and semilinear constraints. For pushdown machines, we show how contributor computations of high stack height can be simulated by computations of many contributors, each with low stack height. Together, our results characterize the complexity of verification for parameterized systems under the assumptions of anonymity and asynchrony.
KeywordsModel checking Shared-memory systems Parametrized verification
Pierre Ganty has been supported by the Madrid Regional Government project S2013/ICE-2731, N-Greens Software - Next-GeneRation Energy-EfficieNt Secure Software, and the Spanish Ministry of Economy and Competitiveness project No. TIN2015-71819-P, RISCO - RIgorous analysis of Sophisticated COncurrent and distributed systems.
- 2.Abdulla PA, Cerans K, Jonsson B, Tsay Y-K (1996) General decidability theorems for infinite-state systems. In: LICS ’96, IEEE Computer Society, Washington, DC, pp 313–321Google Scholar
- 4.Aminof B, Kotek T, Rubin S, Spegni F, Veith H (2014) Parameterized model checking of rendezvous systems. In: CONCUR ’14 Proceedings of the 25th International Conference on Concurrency Theory, vol 704 of LNCS. Springer, Heidelberg, pp 109–124Google Scholar
- 7.Bouajjani A, Esparza J, Maler O (1997) Reachability analysis of pushdown automata: application to model-checking. In: CONCUR ’97 Proceedings of the 8th International Conference on Concurrency Theory, vol 1243 of LNCS. Springer, Heidelberg, pp 135–150Google Scholar
- 8.Esparza J, Finkel A and Mayr R (1999) On the verification of broadcast protocols. In: LICS ’99, IEEE Computer Society, Washington, DC, pp 352–359Google Scholar
- 9.Esparza J, Ganty P, Majumdar R (2013) Parameterized verification of asynchronous shared-memory systems. In: CAV ’13 Proceedings of the 23rd International Conference on Computer Aided Verification, vol 8044 of LNCS. Springer, Heidelberg, pp 124–140Google Scholar
- 13.Hague M (2011) Parameterised pushdown systems with non-atomic writes. In: Proceedings of FSTTCS ’11, vol 13 of LIPIcs. Schloss Dagstuhl, Wadern, pp 457–468Google Scholar
- 14.Meyer R (2008) On boundedness in depth in the pi-calculus. In: Proceedings of IFIP TCS 2008, vol 273 of IFIP. Springer, Heidelberg, pp 477–489Google Scholar
- 15.Pnueli A, Xu J, Zuck LD (2002) Liveness with (0, 1, infty)-counter abstraction. In: CAV ’02 Proceedings of 14th International Conference on Computer Aided Verification, vol 2404 of LNCS. Springer, Heidelberg, pp 107–122Google Scholar
- 16.Torre SL, Muscholl A, Walukiewicz I (2015) Safety of parametrized asynchronous shared-memory systems is almost always decidable. In: CONCUR ’15 Proceedings of 26th International Conference on Concurrency Theory, vol 42 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Wadern, pp 72–84Google Scholar
- 17.Verma KN, Seidl H, Schwentick T (2005) On the complexity of equational horn clauses. In: CADE ’05 20th International Conference on Automated Deduction, vol 1831 of LNCS. Springer, Heidelberg, pp 337–352Google Scholar