Fast Infinite-State Model Checking in Integer-Based Systems
In this paper we discuss the use of logic for reachability analysis for infinite-state systems. Infinite-state systems are formalized using transition systems over a first-order structure. We establish a common ground relating a large class of algorithms by analyzing the connections between the symbolic representation of transition systems and formulas used in various reachability algorithms. We consider in detail the so-called guarded assignment systems and local reachability algorithms. We show how an implementation of local reachability algorithms and a new incremental algorithm for finding Hilbert’s base in the system BRAINresulted in much faster reachability checking than in systems using constraint libraries and decision procedures for Presburger’s arithmetic. Experimental results demonstrate that problems in protocol verification which are beyond the reach of other existing systems can be solved completely automatically.
Unable to display preview. Download preview PDF.
- 4.Beltyukov, A.P.: Decidability of the universal theory of natural numbers with addition and divisibility (in Russian). Zapiski Nauchnyh Seminarov LOMI 60, 15–28 (1976); English translation in Journal of Soviet MathematicsGoogle Scholar
- 5.Bjørner, N.S.: Integrating Decision Procedures for Temporal Verification. PhD thesis, Computer Science Department, Stanford University (1998)Google Scholar
- 6.Bjørner, N.S.: Reactive verification with queues. In: ARO/ONR/NSF/DARPA Workshop on Engineering Automation for Computer-Based Systems, Carmel, CA, pp. 1–8 (1998)Google Scholar
- 13.Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: 14th Annual IEEE Symposium on Logic in Computer Science (LICS 1999), Trento, Italy, pp. 352–359. IEEE Computer Society, Los Alamitos (1999)Google Scholar
- 26.Queille, J.P., Sifakis, J.: Specification and verification of concurrent systems in Cesar. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982)Google Scholar
- 30.Voronkov, A.: An incremental algorithm for finding the basis of solutions to systems of linear Diophantine equations and inequations (January 2003) (unpublished)Google Scholar