Abstract
The linear time mu-calculus vTL is a language extending standard linear time temporal logic with fixpoint operators. We present a method for deciding whether a given vTZ-formula is satisfiable, and give a direct proof of its completeness. Although simpler than the existing methods, it gives rise to an algorithm working in the same 2O(n 2 log n) time as these, or alternatively, to a polynomial space, singly exponential time algorithm. What is more important, the method allows us to devise a tableau system to support manual or computer-aided (as opposed to fully automated) satisfiability checking.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Balcazar, J. L. and; Diaz, J. and; Gabarro. J.: Structural Complexity /, EATCS Monographs on Theoretical Computer Science vol. 11, Springer-Verlag, 1988
Banieqbal, B. and Barringer, H.: Temporal Logic with Fixed Points, in Temporal Logic in Specification, LNCS vol. 398, Springer-Verlag, 1989, pp. 62–74
Barringer, H. and; Kuiper, R. and Pnueli, A.: A Really Abstract Concurrent Model and its Temporal Logic, in Proc. of the 13th ACM POPL, 1986
Büchi, J. R.: On a Decision Method in Restricted Second-Order Arithmetics, in Proc. of the 1960 International Congress on Logic, Methodology and Philosophy of Science, Stanford University Press, 1962, pp. 1–12
Dickson, L. E.: Finiteness of the Odd Perfect and Primitive Abundant Numbers with Distinct Prime Factors, in Americal Journal of Mathematics, vol. 35, 1913, pp. 413–422
Emerson, E. A.: Temporal and Modal Logic, in van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, Elsevier/North-Holland, 1990, pp. 997–1072
Emerson, E. A. h Clarke, E. M.: Characterising Correctness Properties of Parallel Programs using Fixpoints, in Proc. of the 7th ICALP, LNCS vol. 85, Springer- Verlag, 1980, pp. 169–181
Kozen, D.: Results on the Propositional /¿-calculus, in Theoretical Computer Science, vol. 27, 1983, pp. 333–354
Lichtenstein, O.: Decidability, Completeness, and Extensions of Linear Time Temporal Logic, PhD thesis, The Weizmann Institute of Science, Rehovot, Israel, 1991
Lichtenstein, O. and; Pnueli, A. and; Zuck, L.: The Glory of the Past, in Proc. of Workshop on Logics of Programs, LNCS vol. 193, Springer-Verlag, 1985, pp. 97–107
Safra, S.: On the Complexity of u;-Automat a, in Proceedings of the 29th Sym-posium on Foundations of Computer Science, 1988, pp. 319–327
Savitch, W. J.: Relationships Between Nondeterministic and Deterministic Tape Complexities, in Journal of Computer and System Sci., vol. 4, 1970, pp. 177–192
Stirling, C.: Modal and Temporal Logics, in Abramsky, S. and; al. (eds.): Handbook of Logic in Computer Science, Oxford University Press, 1992, pp. 477–563
Streett, R. S. and; Emerson, E. A.: An Automata Theoretic Decision Procedure for the Propositional Mu-Calculus, in Information and Computation, vol. 81, 1989, pp. 249–264
Vardi, M. Y.: A Temporal Fixpoint Calculus, in Proceedings of the 15th ACM Symposium on Priciples of Programming Languages, 1988, pp. 250–259
Wolper, P.: Synthesis of Communicating Processes from Temporal Logic Specifications, PhD thesis, Stanford University, 1982
Wolper, P.: Temporal Logic can be More Expressive, in Information and Control, vol 56, 1983, pp. 72–99
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 British Computer Society
About this paper
Cite this paper
Kaivola, R. (1995). A Simple Decision Method for the Linear Time Mu-calculus. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3078-9_13
Publisher Name: Springer, London
Print ISBN: 978-3-540-19982-3
Online ISBN: 978-1-4471-3078-9
eBook Packages: Springer Book Archive