Abstract
Characteristic formulae have been introduced by Graf and Sifakis to relate equational reasoning about processes to reasoning in a modal logic, and therefore to allow proofs about processes to be carried out in a logical framework. Based upon an intuitionistic understanding of the modal mu-calculus, this paper extends the results of Graf and Sifakis in two respects. First, it covers not only finite processes, but finite state processes. Second, it handles not only bisimulation-like equivalences but also preorders, which are sensitive to liveness properties.
Preview
Unable to display preview. Download preview PDF.
References
E. Clarke, E. A. Emerson and A.P. Sistla. Automatic Verification of Finite State Concurrent Systems using Temporal Logic Specifications: A Practical Approach, ACM 1983
E. Clarke, O. Grumberg and M.C. Browne. Reasoning About Networks With Many Identical Finite-State Processes, Carnegie Mellon University, Pittsburg, October 1986
R. Cleaveland. Tableau-Based Model Checking in the Propositional Mu-Calculus, University of Sussex, Brighton, Technical Report 2–89, 1989
G. Cousineau and M. Nivat. On Rational Expressions Representing Infinite Rational Trees: Application to the Structure of Flow Charts, 8th MFCS, LNCS 74, pp. 567–580, 1979
R. Cleaveland, J. G. Parrow and B. Steffen. The Concurrency Workbench: Operating Instructions, University of Edinburgh, Laboratory for Foundations of Computer Science, Technical Notes 10, September 1988
R. Cleaveland, J. G. Parrow and B. Steffen. The Concurrency Workbench, Accepted for the Workshop on Automatic Verification Methods for Finite State Systems, Grenoble, France, 1989
R. Cleaveland, J. G. Parrow and B. Steffen. A Semantics based Verification Tool for Finite State Systems, to appear in the proceedings of the Ninth International Symposium on Protocol Specification, Testing, and Verification; North Holland, 1989
E. A. Emerson and C.-L. Lei. Efficient Model Checking in Fragments of the Propositional Mu-Calculus, LICS, Cambridge, Mass., IEEE, 1986
S. Graf and J. Sifakis. A Modal Characterization of Observational Congruence on Finite Terms of CCS, Information and Control, pp. 125–145, Vol 68, 1986
S. Holmström. Hennessy-Milner Logic with Recursion as a Specification Language, and a Refinement Calculus based on it, Report 44 Programming Methodology Group, University of Göteborg, 1988
D. Kozen. Results on the Propositional Mu-Calculus, TCS 27, pp. 333–354, North Holland, 1983
K. Larsen. Proof Systems for Hennessy-Milner Logic with Recursion, in Proceedings CAAP 1988
A.R. Meyer and K.A. Winklmann. On the Expressive Power of Dynamic Logics, 11th STOC, ACM, pp. 167–175, 1979
R. Milner. A Calculus for Communicating Systems, LNCS 92
R. Milner. A Modal Characterization of Observable Machine-Behaviour, LNCS 112, pp. 25–34, Berlin 1981
R. Milner. Communication and Concurrency, Prentice Hall, 1989
G. Plotkin and C. Stirling. A Framework for Intuitionistic Modal Logics, Theoretical Aspects of Reasoning about Knowledge, Monterey, 1986
B. Steffen. Characteristic Formulae for CCS with Divergence, University of Edinburgh, Laboratory for Foundations of Computer Science, Technical Report ECS-LFCS-89-76, 1989
C. Stirling. Modal Logics for Communicating Systems, TCS 49, pp. 311–347, 1987
C. Stirling and D. J. Walker. Local Model Checking in the Modal Mu-Calculus, in Proceedings CAAP 1989
D.J. Walker. Bisimulation and Divergence in CCS, in Proceedings LICS 1988
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Steffen, B. (1989). Characteristic formulae. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035794
Download citation
DOI: https://doi.org/10.1007/BFb0035794
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51371-1
Online ISBN: 978-3-540-46201-9
eBook Packages: Springer Book Archive