Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-02T07:24:02.443Z Has data issue: false hasContentIssue false
  • English
  • Français

On global induction mechanisms in a μ-calculus with explicitapproximations

Published online by Cambridge University Press:  15 January 2004

Christoph Sprenger  and
Mads Dam
Christoph Sprenger
Affiliation:
INRIA Sophia Antipolis, 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis, France; sprenger@sophia.inria.fr.
Mads Dam
Affiliation:
Dept. of Microelectronics and Information Technology, Royal Institute of Technology, KTH, Forum 105, 164 40 Kista, Sweden; mfd@imit.kth.se.
Get access

Abstract

We investigate a Gentzen-style proof system for the first-order μ-calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantic condition. We give an automata-theoretic reformulation of this condition which is more suitable for practical proofs. For a detailed comparison with previous work we consider two simpler syntactic conditions and show that they are more restrictive than our new condition.

Keywords

Inductive reasoningcircular proofswell-foundednessglobal consistency conditionμ-calculusapproximants.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 4: Fixed Points in Computer Science (FICS'02) , October 2003 , pp. 365 - 391
Copyright
© EDP Sciences, 2003

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

Arts, T., Dam, M., Fredlund, L. and Gurov, D., System description: Verification of distributed Erlang programs. Lecture Notes in Artificial Intelligence 1421 (1998) 38-41.
Bradfield, J. and Stirling, C., Local model checking for infinite state spaces. Theor. Comput. Sci. 96 (1992) 157-174 . CrossRef
Dam, M., Proving properties of dynamic process networks. Inf. Comput. 140 (1998) 95-114. CrossRef
Dam, M. and Gurov, D., μ-calculus with explicit points and approximations. J. Logic Comput. 12 (2002) 43-57. Previously appeared in Fixed Points in Computer Science, FICS (2000). CrossRef
Emerson, E.A. and Lei, C.L., Modalities for model checking: branching time strikes back. Sci. Comput. Program. 8 (1987) 275-306 . CrossRef
L. Fredlund, A Framework for Reasoning about Erlang Code. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden (2001).
Kozen, D., Results on the propositional μ-calculus. Theor. Comput. Sci. 27 (1983) 333-354 . CrossRef
Niwinski, D. and Walukiewicz, I., Games for the μ-calculus. Theor. Comput. Sci. 163 (1997) 99-116. CrossRef
Park, D., Finiteness is mu-ineffable. Theor. Comput. Sci. 3 (1976) 173-181 . CrossRef
S. Safra, On the complexity of ω-automata, in 29th IEEE Symposium on Foundations of Computer Science (1988) 319-327.
U. Schöpp, Formal verification of processes. Master's thesis, University of Edinburgh (2001)
Schöpp, U. and Simpson, A., Verifying temporal properties using explicit approximants: Completeness for context-free processes, in Foundations of Software Science and Computational Structures (FoSSaCS 02), Grenoble, France. Springer, Lecture Notes in Comput. Sci. 2303 (2002) 372-386. CrossRef
Sprenger, C. and Dam, M., On the structure of inductive reasoning: Circular and tree-shaped proofs in the μ-calculus, Foundations of Software Science and Computational Structures (FoSSaCS 03), Warsaw, Poland, April 7-11 2003. A. Gordon, Springer, Lecture Notes in Comput. Sci. 2620 (2003) 425-440. CrossRef
Stirling, C. and Walker, D., Local model checking in the modal -calculus. Theor. Comput. Sci. 89 (1991) 161-177 . CrossRef
W. Thomas, Automata on infinite objects. J. van Leeuwen, Elsevier Science Publishers, Amsterdam, Handb. Theor. Comput. Sci. B (1990) 133-191.