# Computing behavioural relations, logically

Specification And Verification (Session 3)

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## Abstract

This paper develops a model-checking algorithm for a fragment of the modal mu-calculus and shows how it may be applied to the efficient computation of behavioral relations between processes. The algorithm's complexity is proportional to the product of the size of the process and the size of the formula, and thus improves on the best existing algorithm for such a fixed point logic. The method for computing preorders that the model checker induces is also more efficient than known algorithms.

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## References

- [AC]Arnold, A., and P. Crubille. “A Linear Algorithm To Solve Fixed-Point Equations on Transition Systems.”
*Information Processing Letters*, v. 29, 30 September 1988, pp. 57–66.Google Scholar - [BSV]Boudol, G., de Simone, R. and Vergamini, D. “Experiment with Auto and Autograph on a Simple Case Sliding Window Protocol.” INRIA Report 870, July 1988.Google Scholar
- [CES]Clarke, E.M., E.A. Emerson and Sistla, A.P. “Automatic Verification of Finite State Concurrent Systems Using Temporal Logic Specifications.”
*ACM Transactions on Programming Languages and Systems*, v. 8, n. 2, 1986, pp. 244–263.Google Scholar - [C]Cleaveland, R. “Tableau-Based Model Checking in the Propositional Mu-Calculus.”
*Acta Informatica*, 1990.Google Scholar - [CH]Cleaveland, R. and Hennessy, M.C.B. “Testing Equivalence as a Bisimulation Equivalence.” In
*Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems*. Lecture Notes in Computer Science series 407, Springer-Verlag, Berlin, 1989.Google Scholar - [CPS1]Cleaveland, R., Parrow, J. and Steffen, B. “The Concurrency Workbench.” In
*Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems*, 1989, Lecture Notes in Computer Science 407, pp. 24–37. Springer-Verlag, Berlin.Google Scholar - [CPS2]Cleaveland, R., Parrow, J. and B. Steffen.
*A Semantics based Verification Tool for Finite State Systems*, In pro. of the Ninth International Symposium on Protocol Specification, Testing, and Verification; North Holland, 1989.Google Scholar - [CS]Cleaveland, R. and Steffen, B. “When is ‘Partial’ Complete? A Logic-Based Proof Technique using Partial Specifications.” In Proceedings LICS'90, 1990.Google Scholar
- [DH]DeNicola, R. and Hennessy, M.C.B. “Testing Equivalences for Processes.”
*Theoretical Computer Science*24, 1984, pp. 83–113.Google Scholar - [EL]Emerson, E.A. and Lei, C.-L. “Efficient Model Checking in Fragments of the Propositional Mu-Calculus.” In
*Proceedings of the First Annual Symposium on Logic in Computer Science*, 1986, pp. 267–278.Google Scholar - [Fe]Fernandez, J.-C.
*Aldébaran: Une Système de Vérification par Réduction de Processus Communicants*. Ph.D. Thesis, Université de Grenoble, 1988.Google Scholar - [GS]Graf, S. and Steffen, B. “Using Interface Specifications for Compositional Reduction.” To appear in
*Proceedings of the Workshop on Computer-Aided Verification*.Google Scholar - [Ko]Kozen, D. “Results on the Propositional μ-Calculus.”
*Theoretical Computer Science*, v. 27, 1983, pp. 333–354.Google Scholar - [La]Larsen, K.G. “Proof Systems for Hennessy-Milner Logic with Recursion.” In
*Proceedings of CAAP*, 1988.Google Scholar - [MSGS]Malhotra, J., Smolka, S.A., Giacalone, A. and Shapiro, R. “Winston: A Tool for Hierarchical Design and Simulation of Concurrent Systems.” In
*Proceedings of the Workshop on Specification and Verification of Concurrent Systems*, University of Stirling, Scotland, 1988.Google Scholar - [Mi1]Milner, R.
*A Calculus of Communicating Systems*. Lecture Notes in Computer Science 92. Springer-Verlag, Berlin, 1980.Google Scholar - [Mi2]Milner, R.
*Communication and Concurrency*, Prentice Hall, 1989.Google Scholar - [PS]Plotkin, G. and Stirling, C. “A Framework for Intuitionistic Modal Logics.” Theoretical Aspects of Reasoning about Knowledge, Monterey, 1986.Google Scholar
- [RRSV]Richier, J., Rodriguez, C., Sifakis, J. and Voiron, J. “Verification in XESAR of the Sliding Window Protocol.” In
*Proceedings of the Seventh IFIP Symposium on Protocol Specification, Testing, and Verification*, 1987, North-Holland.Google Scholar - [Ste]Steffen, B.U. “Characteristic Formulae for CCS with Divergence.” In
*Proceedings ICALP*, Lecture Notes in Computer Science 372, pp. 723–733. Springer-Verlag, Berlin, 1989.Google Scholar - [SI]Steffen, B.U., and Ingólfsdóttir, A. “Characteristic Formulae for CCS with Divergence.” To appear in
*Theoretical Computer Science*.Google Scholar - [Sti]Stirling, C. “Modal Logics for Communicating Systems.”
*Theoretical Computer Science*, v. 49, 1987, pp. 311–347.Google Scholar - [SW]Stirling, C., and Walker, D. “Local Model Checking in the Modal Mu-Calculus.” In Proceedings CAAP'89, Lecture Notes in Computer Science 351, pp. 369–383, 1989.Google Scholar
- [Ta]Tarski, A. “A Lattice-Theoretical Fixpoint Theorem and its Applications.”
*Pacific Journal of Mathematics*, v. 5, 1955.Google Scholar - [Wa]Walker, D. “Bisimulations and Divergence.” In
*Proceedings of the Third Annual Symposium on Logic in Computer Science*, 1988, pp. 186–192. Computer Society Press, Washington DC.Google Scholar - [Wi]Winskel, G. “On the Compositional Checking of Validity.” In Proceedings CONCUR'90, Lecture Notes in Computer Science 458, pp. 481–501, 1990.Google Scholar

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© Springer-Verlag Berlin Heidelberg 1991