Abstract
It is known that LTL formulae without the ‘next’ operator are invariant under the so-called stutter-equivalence of words. In this paper we extend this principle to general LTL formulae with given nesting depths of the ‘next’ and ‘until’ operators. This allows us to prove the semantical strictness of three natural hierarchies of LTL formulae, which are parametrized either by the nesting depth of just one of the two operators, or by both of them. As another interesting corollary we obtain an alternative characterization of LTL languages, which are exactly the regular languages closed under the generalized form of stutter equivalence. We also indicate how to tackle the state-space explosion problem with the help of presented results
Supported by the Grant Agency of Czech Republic, grant No. 201/00/1023.
Supported by the Grant Agency of Czech Republic, grant No. 201/00/0400, and by a grant FRVŠ No. 601/2002.
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
E.M. Clark, O. Grumberg, and D.A. Peled. Model Checking. The MIT Press, 1999.
K. Etessami and T. Wilke. An until hierarchy and other applications of an Ehrenfeucht-FraΫissé game for temporal logic. Information and Computation, 160:88–108, 2000.
H. Kamp. Tense Logic and the Theory of Linear Order. PhD thesis, UCLA, 1968.
L. Lamport. What good is temporal logic? In Proceedings of IFIP Congress on Information Processing, pages 657–667, 1983.
R. McNaughton and S. Papert. Counter-Free Automata. The MIT Press, 1971.
A. Pnueli. The temporal logic of programs. In Proceedings of 18th Annual Symposium on Foundations of Computer Science, pages 46–57. IEEE Computer Society Press, 1977.
W. Thomas. Automata on infinite objects. Handbook of Theoretical Computer Science, B:135–192, 1991.
T. Wilke. Classifying discrete temporal properties. In Proceedings of STACS’99, volume 1563 of LNCS, pages 32–46. Springer, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kucera, A., Strejček, J. (2002). The Stuttering Principle Revisited: On the Expressiveness of Nested X and ⋃ Operators in the Logic LTL. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_19
Download citation
DOI: https://doi.org/10.1007/3-540-45793-3_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44240-0
Online ISBN: 978-3-540-45793-0
eBook Packages: Springer Book Archive