article

Experiments with deterministic ω-automata for formulas of linear temporal logic

Authors:

Christel BaierAuthors Info & Claims

Theoretical Computer Science, Volume 363, Issue 2

Pages 182 - 195

https://doi.org/10.1016/j.tcs.2006.07.022

Published: 28 October 2006 Publication History

Abstract

This paper addresses the problem of generating deterministic ω-automata for formulas of linear temporal logic, which can be solved by applying well-known algorithms to construct a nondeterministic Büchi automaton for the given formula on which we then apply a determinization algorithm. We study here in detail Safra's determinization algorithm, present several heuristics that attempt to decrease the size of the resulting automata and report on experimental results.

References

[1]

{1} C.S. Althoff, W. Thomas, N. Wallmeier, Observations on determinization of Büchi automata, in: CIAA'05, Proc. Lecture Notes in Computer Science, Vol. 3845, Springer, Berlin, 2006, pp. 262-272.]]

Digital Library

[2]

{2} C. Baier, M. Kwiatkowska, Model checking for a probabilistic branching time logic with fairness, Distributed Comput. 11 (1998) 125-155.]]

Digital Library

[3]

{3} L. de Alfaro, Formal verification of probabilistic systems, Ph.D. Thesis, Department of Computer Science, Stanford University, Stanford, 1997.]]

[4]

{4} M.B. Dwyer, G.S. Avrunin, J.C. Corbett, Patterns in property specifications for finite-state verification, in: ICSE, 1999, pp. 411-420.]]

Digital Library

[5]

{5} E.A. Emerson, A.P. Sistla, Deciding branching time logic, in: STOC'84, ACM, New York, 1984, pp. 14-24.]]

Digital Library

[6]

{6} K. Etessami, G.J. Holzmann, Optimizing Büchi automata, in: CONCUR, Lecture Notes in Computer Science, Vol. 1877, Springer, Berlin, 2000, pp. 153-167.]]

Digital Library

[7]

{7} K. Etessami, T. Wilke, R.A. Schuller, Fair simulation relations, parity games, and state space reduction for Büchi automata, in: ICALP'2001, Lecture Notes in Computer Science, Vol. 2076, Springer, Berlin, 2001, pp. 694-707.]]

Digital Library

[8]

{8} C. Fritz, Constructing Büchi automata from linear temporal logic using simulation relations for alternating Büchi automata, in: CIAA 2003, Lecture Notes in Computer Science, Vol. 2759, Springer, Berlin, 2003, pp. 35-48.]]

[9]

{9} P. Gastin, D. Oddoux, Fast LTL to Büchi automata translation, in: Computer Aided Verification (CAV'2001), Proc. Lecture Notes in Computer Science, Vol. 2102, Springer, Berlin. 2001, pp. 53-65.]]

Digital Library

[10]

{10} R. Gerth, D. Peled, M.Y. Vardi, P. Wolper, Simple on-the-fly automatic verification of linear temporal logic, in: PSTV'95, Proc. IFIP Conference Proceedings, Vol. 38, Chapman & Hall, London, 1995, pp. 3-18.]]

Digital Library

[11]

{11} E. Grädel, W. Thomas, T. Wilke (Eds.), Automata logics, and infinite games: a guide to current research, Lecture Notes in Computer Science, Vol. 2500, Springer, Berlin, 2002.]]

Digital Library

[12]

{12} G.J. Holzmann, The model checker spin, IEEE Trans. Software Eng. 23 (5) (1997) 279-295, (special issue on Formal Methods in Software Practice).]]

Digital Library

[13]

{13} J. Klein, Linear time logic and deterministic omega-automata, Diploma Thesis, Universität Bonn, Institut für Informatik, 2005.]]

[14]

{14} S.C. Krishnan, A. Puri, R.K. Brayton, Deterministic ω automata vis-a-vis deterministic Buchi automata, in: Algorithms and Computation, Fifth International Symposium (ISAAC'94), Lecture Notes in Computer Science, Vol. 834, Springer, Berlin, 1994, pp. 378-386.]]

Digital Library

[15]

{15} O. Kupferman, M.Y. Vardi, Freedom, weakness, and determinism: from lineartime to branching--time, in: Proc. 13th IEEE Symposium on Logic in Computer Science, 1998, pp. 81-92.]]

Digital Library

[16]

{16} O. Kupferman, M.Y. Vardi, Model checking of safety properties, in: Computer Aided Verification (CAV'99), Proc. Lecture Notes in Computer Science, Vol. 1633, Springer, Berlin, 1999, pp. 172-183.]]

Digital Library

[17]

{17} T. Latvala, On model checking safety properties, Research Report A76, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland, 2002.]]

[18]

{18} C. Löding, Methods for the transformation of omega-automata: complexity and connection to second order logic, Diploma Thesis, Universität Kiel, Germany, 1998.]]

[19]

{19} C. Löding, Optimal bounds for the transformation of omega-automata, in: FSTTCS'99, Lecture Notes in Computer Science, Vol. 1738, Springer, Berlin, 1999, pp. 97-109.]]

Digital Library

[20]

{20} C. Löding, Efficient minimization of deterministic weak omega-automata, Inform. Process. Lett. 79 (3) (2001) 105-109.]]

Digital Library

[21]

{21} M. Michel, Complementation is more difficult with automata on infinite words, Technical Report CNET, Paris, 1988.]]

[22]

{22} D.E. Muller, P.E. Schupp, Simulating alternating tree automata by nondeterministic automata: new results and new proofs of the theorems of Rabin, McNaughton and Safra, Theoret. Comput. Sci. 141 (1-2) (1995) 69-107.]]

Digital Library

[23]

{23} R. Paige, R.E. Tarjan, Three partition refinement algorithms, SIAM J. Comput. 16 (6) (1987) 973-989.]]

Digital Library

[24]

{24} S. Safra, On the complexity of ω-automata, in: Proc. 29th Annual Symposium on Foundations of Computer Science (FOCS), IEEE Computer Soc. Press, Silver Spring, Berlin, 1988, pp. 319-327.]]

[25]

{25} S. Safra, Complexity of automata on infinite objects, Ph.D. Thesis, The Weizmann Institute of Science, Rehovot, Israel, 1989.]]

[26]

{26} R. Sebastiani, S. Tonetta, "More deterministic" vs. "Smaller" Büchi automata for efficient LTL model checking, in: CHARME 2003, Proc. Lecture Notes in Computer Science, Vol. 2860, Springer, Berlin, 2003, pp. 126-140.]]

[27]

{27} F. Somenzi, R. Bloem, Efficient Büchi automata from LTL formulae, in: Computer Aided Verification (CAV'2000), Proc. Lecture Notes in Computer Science, Vol. 1855, Springer, Berlin, 2000, pp. 248-263.]]

Digital Library

[28]

{28} S. Tasiran, R. Hojati, R.K. Brayton, Language containment of nondeterministic ω-automata, in: CHARME'95, Lecture Notes in Computer Science, Vol. 987, Springer, Berlin, 1995, pp. 261-277.]]

Digital Library

[29]

{29} H. Tauriainen, Automated testing of Büchi automata translators for linear temporal logic, Research Report, Laboratory for Theoretical Computer Science, Helsinki University of Technology, December 2000.]]

[30]

{30} W. Thomas, Languages, automata, and logic, Handbook of Formal Languages 3 (1997) 389-455.]]

Digital Library

[31]

{31} M. Vardi, Probabilistic linear-time model checking: an overview of the automata-theoretic approach, in: Proc. Formal Methods for Real-Time and Probabilistic Systems (ARTS), Vol. 1601, 1999, pp. 265-276.]]

Digital Library

Cited By

Neupane AGoodrich MMercer E(2023)Plan Generation via Behavior Trees Obtained from Goal-Oriented LTLf FormulasAutonomous Agents and Multiagent Systems. Best and Visionary Papers10.1007/978-3-031-56255-6_6(97-122)Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-56255-6_6
Křetínský JMeggendorfer TWaldmann CWeininger M(2022)Index appearance record with preordersActa Informatica10.1007/s00236-021-00412-y59:5(585-618)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00236-021-00412-y
Esparza J(2021)Back to the Future: A Fresh Look at Linear Temporal LogicImplementation and Application of Automata10.1007/978-3-030-79121-6_1(3-13)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-79121-6_1
Show More Cited By

Index Terms

Experiments with deterministic ω-automata for formulas of linear temporal logic

Recommendations

On Ω-automata and temporal logic
STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to Büchi, Streett, and Emerson and Lei (...
Efficient determinization of visibly and height-deterministic pushdown automata

New algorithms for the determinization of nondeterministic visibly and nondeterministic real-time height-deterministic pushdown automata are presented. The algorithms improve the results of existing algorithms. They construct only accessible states and ...
Watson-Crick ω-automata

Watson-Crick ω-automata are finite automata working with infinite double-stranded words, where the two strands relate to each other through a complementary relation inspired by the DNA complementarity. There are several natural possibilities to define ...

Comments

Information & Contributors

Information

Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 363, Issue 2

Implementation and application of automata

28 October 2006

140 pages

ISSN:0304-3975

Issue’s Table of Contents

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 28 October 2006

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

31
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 26 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Neupane AGoodrich MMercer E(2023)Plan Generation via Behavior Trees Obtained from Goal-Oriented LTLf FormulasAutonomous Agents and Multiagent Systems. Best and Visionary Papers10.1007/978-3-031-56255-6_6(97-122)Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-56255-6_6
Křetínský JMeggendorfer TWaldmann CWeininger M(2022)Index appearance record with preordersActa Informatica10.1007/s00236-021-00412-y59:5(585-618)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00236-021-00412-y
Esparza J(2021)Back to the Future: A Fresh Look at Linear Temporal LogicImplementation and Application of Automata10.1007/978-3-030-79121-6_1(3-13)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-79121-6_1
Esparza JKřetínský JSickert S(2020)A Unified Translation of Linear Temporal Logic to ω-AutomataJournal of the ACM10.1145/341799567:6(1-61)Online publication date: 17-Oct-2020
https://dl.acm.org/doi/10.1145/3417995
Baier CBlahoudek FDuret-Lutz AKlein JMüller DStrejček J(2019)Generic Emptiness Check for Fun and ProfitAutomated Technology for Verification and Analysis10.1007/978-3-030-31784-3_26(445-461)Online publication date: 28-Oct-2019
https://dl.acm.org/doi/10.1007/978-3-030-31784-3_26
Křetínský JManta AMeggendorfer T(2019)Semantic Labelling and Learning for Parity Game Solving in LTL SynthesisAutomated Technology for Verification and Analysis10.1007/978-3-030-31784-3_24(404-422)Online publication date: 28-Oct-2019
https://dl.acm.org/doi/10.1007/978-3-030-31784-3_24
Dutreix MCoogan S(2018)Satisfiability Bounds for co-regular Properties in Interval-valued Markov Chains2018 IEEE Conference on Decision and Control (CDC)10.1109/CDC.2018.8619756(1047-1052)Online publication date: 17-Dec-2018
https://dl.acm.org/doi/10.1109/CDC.2018.8619756
Klein JBaier CChrszon PDaum MDubslaff CKlüppelholz SMärcker SMüller D(2018)Advances in probabilistic model checking with PRISMInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-017-0456-320:2(179-194)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s10009-017-0456-3
Sadraddini SBelta C(2017)Formal methods for adaptive control of dynamical systems2017 IEEE 56th Annual Conference on Decision and Control (CDC)10.1109/CDC.2017.8263906(1782-1787)Online publication date: 12-Dec-2017
https://dl.acm.org/doi/10.1109/CDC.2017.8263906
Kini DViswanathan M(2017)Optimal Translation of LTL to Limit Deterministic AutomataProceedings, Part II, of the 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems - Volume 1020610.1007/978-3-662-54580-5_7(113-129)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54580-5_7
Show More Cited By

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents