Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T22:04:43.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Modal logic and the approximation induction principle

Published online by Cambridge University Press:  28 February 2012

MACIEJ GAZDA  and
WAN FOKKINK
MACIEJ GAZDA
Affiliation:
Eindhoven University of Technology, Department of Computer Science, P.O.Box 513, 5600 MB Eindhoven, The Netherlands Email: m.w.gazda@tue.nl
WAN FOKKINK
Affiliation:
VU University Amsterdam, Department of Computer Science, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands Email: wanf@cs.vu.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove a compactness theorem in the context of Hennessy–Milner logic and use it to derive a sufficient condition on modal characterisations for the approximation induction principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators. Furthermore, we derive different upper bounds for the constructive version of the approximation induction principle with respect to simulation and decorated trace semantics.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Special Issue 2: Express '09, Ice '09 and Sos '09 , April 2012 , pp. 175 - 201
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aceto, L., Bloom, B. and Vaandrager, F. (1994) Turning SOS rules into equations. Information and Computation 111 (1)1–52.CrossRefGoogle Scholar
Aceto, L., Ingolfsdottir, A. and Sack, J. (2009) Characteristic formulae for fixed-point semantics: A general framework. Proc. 16th Workshop on Expressiveness in Concurrency (EXPRESS'09). Electronic Proceedings in Theoretical Computer Science 8 1–15.CrossRefGoogle Scholar
Baeten, J. C. M., Bergstra, J. A. and Klop, J. W. (1987) On the consistency of Koomen's fair abstraction rule. Theoretical Computer Science 51 (1-2)129–176.CrossRefGoogle Scholar
Barros, A. and Hou, T. (2008) A Constructive Version of AIP Revisited. Electronic Report PRG0802, Programming Research Group, University of Amsterdam.Google Scholar
Baeten, J. C. M. and Weijland, W. P. (1990) Process Algebra, Cambridge Tracts in Theoretical Computer Science 18, Cambridge University Press.CrossRefGoogle Scholar
Blackburn, P., de Rijke, M. and Venema, Y. (2001) Modal Logic, Cambridge University Press.CrossRefGoogle Scholar
Bloom, B., Fokkink, W. J. and van Glabbeek, R. J. (2004) Precongruence formats for decorated trace semantics. ACM Transactions on Computational Logic 5 (1)26–78.CrossRefGoogle Scholar
Celikkan, U. and Cleaveland, R. (1995) Generating diagnostic information for behavioral preorders. Distributed Computing 9 (2)61–75.CrossRefGoogle Scholar
van Glabbeek, R. J. (1987) Bounded nondeterminism and the approximation induction principle in process algebra. Proc. 4th Symposium on Theoretical Aspects of Computer Science (STACS'87). Springer-Verlag Lecture Notes in Computer Science 247 336–347.CrossRefGoogle Scholar
van Glabbeek, R. J. (1993) The linear time/branching time spectrum II. The semantics of sequential systems with silent moves. Proc. 4th Conference on Concurrency Theory (CONCUR'93). Springer-Verlag Lecture Notes in Computer Science 715 66–81.CrossRefGoogle Scholar
van Glabbeek, R. J. (2001) The linear time/branching time spectrum I. The semantics of concrete, sequential processes. In: Bergstra, J. A., Ponse, A. and Smolka, S. A. (eds.) Handbook of Process Algebra 3–99.Google Scholar
van Glabbeek, R. J. and Ploeger, B. (2008) Correcting a space-efficient simulation algorithm. Proc. 20th Conference on Computer Aided Verification (CAV 2008). Springer-Verlag Lecture Notes in Computer Science 5123 517–529.CrossRefGoogle Scholar
Goldblatt, R. (1995) Saturation and the Hennessy–Milner property. In: Ponse, A., de Rijke, M. and Venema, Y. (eds.) Modal Logic and Process Algebra. A Bisimulation Perspective. CSLI Lecture Notes 53 189–216.Google Scholar
Hennessy, M. and Milner, R. (1985) Algebraic laws for non-determinism and concurrency. Journal of the ACM 32 (1)137–161.CrossRefGoogle Scholar
Hennessy, M. and Milner, R. (1980) On observing nondeterminism and concurrency. Proc. 7th Colloquium on Automata, Languages and Programming (ICALP'80). Springer-Verlag Lecture Notes in Computer Science 85 299–309.CrossRefGoogle Scholar
Hollenberg, M. (1995) Hennessy–Milner classes and process algebra. In: Ponse, A., de Rijke, M. and Venema, Y. (eds.) Modal Logic and Process Algebra. A Bisimulation Perspective. CSLI Lecture Notes 53 189–216.Google Scholar
Larsen, K. (1990) Proof systems for satisfiability in Hennessy–Milner logic with recursion. Theoretical Computer Science 72 (2-3)265–288.CrossRefGoogle Scholar
Mauw, S. (1987) A constructive version of the approximation induction principle. Proc. SION Conference on Computing Science in the Netherlands (CSN'87) 235–252.Google Scholar
Stirling, C. (2001) Modal and Temporal Properties of Processes, Texts in Computer Science, Springer-Verlag.CrossRefGoogle Scholar
Stockmeyer, L. J. and Meyer, A. R. (1973) Word problems requiring exponential time. Proc. 5th Annual ACM Symposium on Theory of Computing (STOC'73) 1–9.Google Scholar