Abstract
In this paper we propose a distributed symbolic algorithm for model checking of propositional μ-calculus formulas. μ-calculus is a powerful formalism and many problems like (fair) CTL and LTL model checking can be solved using the μ-calculus model checking. Previous works on distributed symbolic model checking were restricted to reachability analysis and safety properties. This work thus significantly extends the scope of properties that can be verified for very large designs.
The algorithm distributively evaluates subformulas. It results in sets of states which are evenly distributed among the processes.We show that this algorithm is scalable, and thus can be implemented on huge distributed clusters of computing nodes. In this way, the memory modules of the computing nodes collaborate to create a very large store, thus enables the checking of much larger designs. We formally prove the correctness of the parallel algorithm. We complement the distribution of the state sets by showing how to distribute the transition relation.
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S. Ben-David, T. Heyman, O. Grumberg, and A. Schuster. Scalable Distributed On-the-Fly Symbolic Model Checking. In Third International Conference on Formal methods in Computer-Aided Design (FMCAD’00), Austin, Texas, November 2000.
R. E Bryant. Graph-based Algorithms for Boolean FunctionManipulation. IEEE Transactions on Computers, C-35(8):677–691, 1986.
J. R. Burch, E. M. Clarke, and D. E. Long. Symbolic Model Checking with Partitioned Transition Relations. In A. Halaas and P. B. Denyer, editors, Proceedings of the 1991 International Conference on Very Large Scale Integration, August 1991.
J. R. Burch, E. M. Clarke, K. L. McMillan, D. L. Dill, and L. J. Hwang. Symbolic Model Checking: 1020 States and Beyond. Information and Computation, 98(2):142–170, 1992.
E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. In Proceedings of the Tenth Annual ACM Symposium on Principles of Programming Languages, January 1983.
E.M. Clarke, O. Grumberg, and D.A. Peled. Model Checking. MIT press, December 1999.
R. Cleaveland. Tableau-basedmodel checking in the propositional mu-calculus. Acta Informatica, 27:725–747, 1990.
O. Coudert, J. C. Madre, and C. Berthet. Verifying of Synchronous Sequential Machines Based on Symbolic Execution. In J. Sifakis, editor, Workshop on Automatic Verification Methods for Finite State Systems, pages 365–373. Springer-Verlag, Grenoble, France, 1989.
E. A. Emerson and C.-L. Lei. Efficient Model Checking in Fragments of the Propositional Mu-calculus. In Proceedings of the First Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, June 1986.
T. Heyman, D. Geist, O. Grumberg, and A. Schuster. Achieving Scalability in Parallel Reachability Analysis of Very Large Circuits. In Proc. of the 12th International Conference on Computer Aided Verification. Springer-Verlag, June 2000.
D. Kozen. Results on the propositional μ-calculus. TCS, 27, 1983.
O. Lichtenstein and A. Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In Proceedings of the Twelfth Annual ACM Symposium on Principles of Programming Languages, pages 97–107, January 1985.
D. Long, A. Browne, E. Clark, S. jha, and W. Marrero. An Improved Algorithm for the Evaluation of Fixpoint Expressions. In Proc. of the Sixth International Conference on Computer Aided Verification, LNCS 818, pages 338–350. Springer-Verlag, 1994.
A. Narayan, A. Isles, J. Jain, R. Brayton, and A. L. Sangiovanni-Vincentelli. Reachability Analysis Using Partitioned-ROBDDs. In Proceedings of the IEEE International Conference on Computer Aided Design, pages 388–393. IEEE Computer Society Press, June 1997.
J.P. Quielle and J. Sifakis. Specification and verification of concurrent systems in CESAR. In Proceedings of the Fifth International Symposium in Programming, 1981.
C. Stirling and D. J. Walker. Local Model Checking in the Model Mu-Calculus. In Proc. of the 1989 Int. Joint Conf. on Theory and Practice of Software Development, 1989.
A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math, 1955.
G. Winskel. Model checking in the modal μ-calculus. In Proceedings of the Sixteenth International Colloquium on Automata, Languages, and Programming, 1989.
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Grumberg, O., Heyman, T., Schuster, A. (2001). Distributed Symbolic Model Checking for μ-Calculus. In: Berry, G., Comon, H., Finkel, A. (eds) Computer Aided Verification. CAV 2001. Lecture Notes in Computer Science, vol 2102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44585-4_32
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DOI: https://doi.org/10.1007/3-540-44585-4_32
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