Abstract
We develop a model-checking algorithm that decides for a given context-free process whether it satisfies a property written in the alternation-free modal mu-calculus. The central idea behind this algorithm is to raise the standard iterative model-checking techniques to higher order. in contrast to the usual approaches, in which the set of formulas that are satisfied by a certain state are iteratively computed, our algorithm iteratively computes a property transformer for each state class of the finite process representation. These property transformers can then simply be applied to solve the model-checking problem. The complexity of our algorithm is linear in the size of the system's representation and exponential in the size of the property being investigated.
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J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages. In PARLE '87, LNCS 259, pages 94–113. Springer, 1987.
J.C. Bradfield. Verifying Temporal Properties of Systems with Applications to Petri Nets. PhD thesis, University of Edinburgh, 1991.
R.E. Bryant. Graph-Based Algorithms for Boolean Function Manipulation. IEEE Transactions on Computers, C-35(8):677–691, 1986.
J.C. Bradfield and C. Stirling. Local Model Checking for Infinite State Spaces. Technical Report ECS-LFCS-90-115, LFCS, June 1991.
D. Caucal. Graphes Canoniques de Graphes Algébriques. RAIRO, 24(4):339–352, 1990.
R. Cleaveland, M. Dreimüller, and B. Steffen. Faster Model Checking for the Modal Mu-Calculus. Accepted for CAV '92.
E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic Verification of Finite State Concurrent Systems Using Temporal Logic Specifications. ACM Transactions on Programming Languages and Systems, 8(2):244–263, 1986.
R. Cleaveland. Tableau-Based Model Checking in the Propositional Mu-Calculus. Acta Informatica, 27:725–747, 1990.
R. Cleaveland, J. Parrow, and B. Steffen. The Concurrency Workbench. In Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems, LNCS 407, pages 24–37. Springer, 1989.
R. Cleaveland and B. Steffen. Computing Behavioural Relations, Logically. In ICALP '91, LNCS 510. Springer, 1991.
R. Cleaveland and B. Steffen. A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus. In CAV '91, LNCS 575, pages 48–58. Springer, 1992.
E.A. Emerson and C.-L. Lei. Efficient Model Checking in Fragments of the Propositional Mu-Calculus. In Proc. 1th Annual Symp. on Logic in Computer Science, pages 267–278. IEEE Computer Society Press, 1986.
J.F. Groote. A Short Proof of the Decidability of Bisimulation for Normed bpa-Processes. Technical Report CS-R9151, CWI, December 1991.
H. Hüttel and C. Stirling. Actions Speak Louder than Words: Proving Bisimularity for Context-Free Processes. In Proc. 6th Annual Symp. on Logic in Computer Science, pages 376–386. IEEE Computer Society Press, 1991.
D.T. Huynh and L. Tian. Deciding Bisimilarity of Normed Context-Free Processes is in ∑ p2 . Technical Report UTDCS-1-92, University of Texas at Dallas, 1992.
D. Kozen. Results on the Propositional μ-Calculus. Theoretical Computer Science, 27:333–354, 1983.
K.G. Larsen. Proof Systems for Hennessy-Milner Logic with Recursion. In CAAP '88, LNCS 299, pages 215–230. Springer, 1988.
C. Stirling and D. Walker. Local Model Checking in the Modal Mu-Calculus. In TAPSOFT '89, LNCS 351, pages 369–383. Springer, 1989.
A. Tarski. A Lattice-Theoretical Fixpoint Theorem and its Applications. Pacific Journal of Mathematics, 5:285–309, 1955.
G. Winskel. A Note on Model Checking the Modal Mu-Calculus. In Automata, Languages and Programming, LNCS 372, pages 761–772. Springer, 1989.
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© 1992 Springer-Verlag Berlin Heidelberg
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Burkart, O., Steffen, B. (1992). Model checking for context-free processes. In: Cleaveland, W. (eds) CONCUR '92. CONCUR 1992. Lecture Notes in Computer Science, vol 630. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0084787
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DOI: https://doi.org/10.1007/BFb0084787
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