research-article

Presburger liveness verification of discrete timed automata

Authors:

Pierluigi San Pietro,

Richard A. KemmererAuthors Info & Claims

Theoretical Computer Science, Volume 299, Issue 1

Pages 413 - 438

https://doi.org/10.1016/S0304-3975(02)00485-1

Published: 18 April 2003 Publication History

Abstract

Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decidable, given a discrete timed automaton A and a Presburger property P, whether there exists an -path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each -path of A. These results might give insights into the corresponding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.

References

[1]

R. Alur, Timed automata, in: Lecture Notes in Computer Science, Vol. 1633, Springer, Berlin, 1999, pp. 8-22.

[2]

R. Alur, C. Courcoubetis, D. Dill, Model-checking in dense real time, Inform. Comput., 104 (1993) 2-34.

Digital Library

[3]

R. Alur, D. Dill, A theory of timed automata, Theoret. Comput. Sci., 126 (1994) 183-236.

Digital Library

[4]

R. Alur, T. Feder, T.A. Henzinger, The benefits of relaxing punctuality, J. ACM, 43 (1996) 116-146.

Digital Library

[5]

R. Alur, T.A. Henzinger, Real-time logics, Inform. Comput., 104 (1993) 35-77.

Digital Library

[6]

R. Alur, T.A. Henzinger, A really temporal logic, J. ACM, 41 (1994) 181-204.

Digital Library

[7]

A. Bouajjani, S. Tripakis, S. Yovine, On-the-fly symbolic model-checking for real-time systems, in: Proc. 18th Real Time Systems Symposium (RTSS¿97), IEEE Computer Society Press, Silver Spring, MD, 1997, pp. 25-35.

[8]

A. Coen-Porisini, C. Ghezzi, R. Kemmerer, Specification of real-time systems using ASTRAL, IEEE Trans. Software Eng., 23 (1997) 572-598.

Digital Library

[9]

H. Comon, V. Cortier, Flatness is not a weakness, in: Lecture Notes in Computer Science, Vol. 1862, Springer, Berlin, 2000, pp. 262-276.

[10]

H. Comon, Y. Jurski, Timed automata and the theory of real numbers, in: Lecture Notes in Computer Science, Vol. 1664, Springer, Berlin, 1999, pp. 242-257.

[11]

Z. Dang, Binary reachability analysis of pushdown timed automata with dense clocks, in: Lecture Notes in Computer Science, Vol. 2102, Springer, Berlin, 2001, pp. 506-517.

[12]

Z. Dang, O.H. Ibarra, T. Bultan, R.A. Kemmerer, J. Su, Binary reachability analysis of discrete pushdown timed automata, in: Lecture Notes in Computer Science, Vol. 1855, Springer, Berlin, 2000, pp. 69-84.

[13]

Z. Dang, P. San Pietro, R.A. Kemmerer, On Presburger liveness of discrete timed automata, in: Lecture Notes in Computer Science, Vol. 2010, Springer, Berlin, 2001, pp. 132-143.

[14]

C. Dima, An algebraic theory of real-time formal languages, Ph.D. Dissertation, Verimag, Grenoble, 2001.

[15]

C. Heitmeyer, N. Lynch, The generalized railroad crossing, in: Proc. 15th Real-time Systems Symposium (RTSS¿94), IEEE Computer Society Press, Silver Spring, MD, 1994, pp. 120-131.

[16]

T.A. Henzinger, Z. Manna, A. Pnueli, What good are digital clocks?, in: Lecture Notes in Computer Science, Vol. 623, Springer, Berlin, 1992, pp. 545-558.

[17]

T.A. Henzinger, X. Nicollin, J. Sifakis, S. Yovine, Symbolic model checking for real-time systems, Inform. Comput., 111 (1994) 193-244.

Digital Library

[18]

T.A. Henzinger, Pei-Hsin Ho, HyTech: the Cornell hybrid technology tool, in: Lecture Notes in Computer Science, Vol. 999, Springer, Berlin, 1995, pp. 265-294.

[19]

O.H. Ibarra, Reversal-bounded multicounter machines and their decision problems, J. ACM, 25 (1978) 116-133.

Digital Library

[20]

F. Laroussinie, K.G. Larsen, C. Weise, From timed automata to logic¿and back, in: Lecture Notes in Computer Science, Vol. 969, Springer, Berlin, 1995, pp. 529-539.

[21]

K.G. Larsen, P. Pattersson, W. Yi, UPPAAL in a nutshell, Internat. J. Software Tools Technol. Transfer, 1 (1997) 134-152.

Digital Library

[22]

J. Raskin, P. Schobben, State clock logic, in: Lecture Notes in Computer Science, Vol. 1201, Springer, Berlin, 1997, pp. 33-47.

[23]

V. Weispfenning, The complexity of almost linear Diophantine problems, J. Symb. Comp., 10 (1990) 395-403.

Digital Library

[24]

T. Wilke, Specifying timed state sequences in powerful decidable logics and timed automata, Lecture Notes in Computer Science, Vol. 863, Springer, Berlin, 1994, pp. 694-715.

[25]

S. Yovine, Kronos, Internat. J. Software Tools Technol. Transfer, 1 (1997) 123-133.

Digital Library

[26]

S. Yovine, Model checking timed automata, in: Lecture Notes in Computer Science, Vol. 1494, Springer, Berlin, 1998, pp. 114-152.

Cited By

Demri S(2006)LTL Over integer periodicity constraintsTheoretical Computer Science10.1016/j.tcs.2006.02.019360:1(96-123)Online publication date: 21-Aug-2006
https://dl.acm.org/doi/10.1016/j.tcs.2006.02.019
Demri SFinkel AGoranko Vvan Drimmelen G(2006)Towards a model-checker for counter systemsProceedings of the 4th international conference on Automated Technology for Verification and Analysis10.1007/11901914_36(493-507)Online publication date: 23-Oct-2006
https://dl.acm.org/doi/10.1007/11901914_36
Dang ZIbarra OSu J(2005)On composition and lookahead delegation of e-services modeled by automataTheoretical Computer Science10.1016/j.tcs.2005.06.009341:1(344-363)Online publication date: 5-Sep-2005
https://dl.acm.org/doi/10.1016/j.tcs.2005.06.009
Show More Cited By

Index Terms

Presburger liveness verification of discrete timed automata

Recommendations

Past pushdown timed automata and safety verification
Implementation and application automata

We consider past pushdown timed automata that are discrete pushdown timed automata with past formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the ...
Interrupt Timed Automata: verification and expressiveness

We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment.

While the reachability problem is undecidable for ...
On Presburger Liveness of Discrete Timed Automata
STACS '01: Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science

Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a ...

Comments

Information & Contributors

Information

Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 299, Issue 1

April 2003

788 pages

ISSN:0304-3975

Issue’s Table of Contents

Copyright © Elsevier Science B.V.

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 18 April 2003

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
0
Total Downloads

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

Reflects downloads up to 20 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Demri S(2006)LTL Over integer periodicity constraintsTheoretical Computer Science10.1016/j.tcs.2006.02.019360:1(96-123)Online publication date: 21-Aug-2006
https://dl.acm.org/doi/10.1016/j.tcs.2006.02.019
Demri SFinkel AGoranko Vvan Drimmelen G(2006)Towards a model-checker for counter systemsProceedings of the 4th international conference on Automated Technology for Verification and Analysis10.1007/11901914_36(493-507)Online publication date: 23-Oct-2006
https://dl.acm.org/doi/10.1007/11901914_36
Dang ZIbarra OSu J(2005)On composition and lookahead delegation of e-services modeled by automataTheoretical Computer Science10.1016/j.tcs.2005.06.009341:1(344-363)Online publication date: 5-Sep-2005
https://dl.acm.org/doi/10.1016/j.tcs.2005.06.009
Xie GLi CDang Z(2004)Linear reachability problems and minimal solutions to linear Diophantine equation systemsTheoretical Computer Science10.1016/j.tcs.2004.07.015328:1-2(203-219)Online publication date: 29-Nov-2004
https://dl.acm.org/doi/10.1016/j.tcs.2004.07.015
Dang ZIbarra OSu J(2004)Composability of Infinite-State Activity AutomataAlgorithms and Computation10.1007/978-3-540-30551-4_34(377-388)Online publication date: 20-Dec-2004
https://dl.acm.org/doi/10.1007/978-3-540-30551-4_34
Dang ZIbarra OPietro PXie G(2004)Real-Counter automata and their decision problemsProceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science10.1007/978-3-540-30538-5_17(198-210)Online publication date: 16-Dec-2004
https://dl.acm.org/doi/10.1007/978-3-540-30538-5_17

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents