Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-21T01:49:52.442Z Has data issue: false hasContentIssue false

Almost linear Büchi automata

Published online by Cambridge University Press:  28 February 2012

TOMÁŠ BABIAK
Affiliation:
Faculty of Informatics, Masaryk University, Brno, Czech Republic Email: xbabiak@fi.muni.cz, rehak@fi.muni.cz, strejcek@fi.muni.cz
VOJTĚCH ŘEHÁK
Affiliation:
Faculty of Informatics, Masaryk University, Brno, Czech Republic Email: xbabiak@fi.muni.cz, rehak@fi.muni.cz, strejcek@fi.muni.cz
JAN STREJČEK
Affiliation:
Faculty of Informatics, Masaryk University, Brno, Czech Republic Email: xbabiak@fi.muni.cz, rehak@fi.muni.cz, strejcek@fi.muni.cz

Abstract

We introduce a new fragment of linear temporal logic (LTL) called LIO and a new class of Büchi automata (BA) called almost linear Büchi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two formalisms are expressively equivalent. As we expect there to be applications of our results in model checking, we use two standard sources of specification formulae, namely Spec Patterns and BEEM, to study the practical relevance of the LIO fragment, and to compare our translation of LIO to ALBA with two standard translations of LTL to BA using alternating automata. Finally, we demonstrate that the LIO to ALBA translation can be much faster than the standard translation, and the resulting automata can be substantially smaller.

Type
Paper
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

Babiak, T. (2010) Almost linear Büchi automata. Master's thesis, Faculty of Informatics, Masaryk University.CrossRefGoogle Scholar
Babiak, T., Řehák, V. and Strejček, J. (2009) Almost linear Büchi automata. In: EXPRESS 2009. Electronic Proceedings in Theoretical Computer Science 8 1625.CrossRefGoogle Scholar
Barnat, J., Brim, L., Černá, I., Moravec, P., Ročkai, P. and Šimeček, P. (2006) DiVinE – A Tool for Distributed Verification. In: Ball, T. and Jones, R. B. (eds.) Computer Aided Verification: Proceedings 18th International Conference, CAV 2006. Springer-Verlag Lecture Notes in Computer Science 4144 278281.CrossRefGoogle Scholar
Černá, I. and Pelánek, R. (2003) Relating hierarchy of temporal properties to model checking. In: Proceedings of the 30th Symposium on Mathematical Foundations of Computer Science (MFCS'03). Springer-Verlag Lecture Notes in Computer Science 2747 318327.CrossRefGoogle Scholar
Courcoubetis, C., Vardi, M. Y., Wolper, P. and Yannakakis, M. (1992) Memory-efficient algorithms for the verification of temporal properties. Formal Methods in System Design 1 (2/3)275288.CrossRefGoogle Scholar
Dwyer, M. B., Avrunin, G. S. and Corbett, J. C. (1998) Property specification patterns for finite-state verification. In: Proc. 2nd Workshop on Formal Methods in Software Practice (FMSP-98), ACM Press 715.CrossRefGoogle Scholar
Etessami, K. and Holzmann, G. J. (2000) Optimizing Büchi automata. In: Palamidessi, C. (ed.) Proceedings CONCUR 2000 – Concurrency Theory, 11th International Conference. Springer-Verlag Lecture Notes in Computer Science 1877 153167.CrossRefGoogle Scholar
Gastin, P. and Oddoux, D. (2001) Fast LTL to Büchi automata translation. In: Berry, G., Comon, H. and Finkel, A. (eds.) Proceedings of the 13th International Conference on Computer Aided Verification (CAV'01). Springer-Verlag Lecture Notes in Computer Science 2102 5365.CrossRefGoogle Scholar
Holzmann, G., Peled, D. and Yannakakis, M. (1996) On nested depth first search. In: The Spin Verification System, Proceedings of the Second Spin Workshop, American Mathematical Society 2332.Google Scholar
Lamport, L. (1983) What good is temporal logic? In: Mason, R. E. A. (ed.) Proceedings of the IFIP Congress on Information Processing, North-Holland657667.Google Scholar
Maidl, M. (2000) The common fragment of CTL and LTL. In: Young, D. C. (ed.) Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science (FOCS'00), IEEE Computer Society Press 643652.Google Scholar
Manna, Z. and Pnueli, A. (1990) A hierarchy of temporal properties. In: Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC'90), ACM Press 377410.CrossRefGoogle Scholar
Pelánek, R. (2007) BEEM: Benchmarks for explicit model checkers. In: Bosnacki, D. and Edelkamp, S. (eds.) Model Checking Software, Proceedings 14th International SPIN Workshop. Springer-Verlag Lecture Notes in Computer Science 4595 263267.CrossRefGoogle Scholar
Perrin, D. and Pin, J.-E. (2004) Infinite words. Pure and Applied Mathematics 141.Google Scholar
Pnueli, A. (1977) The temporal logic of programs. In: Proceedings 18th IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press 4657.Google Scholar
Rozier, K. Y. and Vardi, M. Y. (2007) LTL satisfiability checking. In: Bosnacki, D. and Edelkamp, S. (eds.) Model Checking Software, Proceedings 14th International SPIN Workshop. Springer-Verlag Lecture Notes in Computer Science 4595 149167.CrossRefGoogle Scholar
Strejček, J. (2004) Linear Temporal Logic: Expressiveness and Model Checking, Ph.D. thesis, Faculty of Informatics, Masaryk University in Brno.Google Scholar
Tarjan, R. E. (1972) Depth-first search and linear graph algorithms. SIAM J. Comput. 1 (2)146160.CrossRefGoogle Scholar