Abstract
To model the behavior of finite-state asynchronous real-time systems we propose the notion of timed Büchi automata (TBA). TBAs are Büchi automata coupled with a mechanism to express constant bounds on the timing delays between system events. These automata accept languages of timed traces, traces in which each event has an associated real-valued time of occurrence.
We show that the class of languages accepted by TBAs is closed under the operations of union, intersection and projections, and the trace language obtained by projecting the language accepted by a TBA is ω-regular. It turns out that TBAs are not closed under complement, and it is undecidable whether the language of one automaton is a subset of the language of another. This result is an obstruction to automatic verification. However, we show that a significant (proper) subclass represented by deterministic timed Muller automata (DTMA) is closed under all the boolean operations. Consequently, a system modeled by a TBA can be automatically verified with respect to a specification given as a DTMA.
Supported by the NSF grant CCR-8812595, and the DARPA contract N00039-84-C-0211, and by the USAF office of Scientific Research under contracts 88-0281 and 90-0057.
Supported by the NSF grant MIP-8858807.
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References
S. Aggarwal, R.P. Kurshan, “Modeling elapsed time in protocol specification,” Protocol Specification, Testing and Verification, III, 1983.
R. Alur, C. Courcoubetis, D.L. Dill, “Model-checking for real-time systems,” 5th IEEE LICS, 1990.
R. Alur, T.A. Henzinger, “Real-time logics: complexity and expressiveness,” 5th IEEE LICS, 1990.
J.R. Büchi, “On a decision method in restricted second-order arithmetic,” Proc. Internat. Congr. Logic, Methodology, and Philosophy of Science 1960, Stanford Univ. Press, 1962.
Y. Choueka, “Theories of automata on ω-tapes: a simplified approach,” JCSS 8, 1974.
E.M. Clarke, I.A. Draghicescu, R.P. Kurshan, “A unified approach for showing language containment and equivalence between various types of ω-automata,” Tech. report CMU-CS-89-192, Carnegie Mellon University, 1989.
E.M. Clarke, E.A. Emerson, A.P. Sistla, “Automatic verification of finite-state concurrent systems using temporal logic specifications,” ACM TOPLAS 8(2), 1986.
D.L. Dill, Trace Theory for Automatic Hierarchical Verification of Speed Independent Circuits, Ph.D. Thesis, Carnegie Mellon Univ., 1988.
D.L. Dill, “Timing assumptions and verification of finite-state concurrent systems,” Automatic Verification Methods for Finite State Systems, LNCS 407, 1989.
C.A.R. Hoare, Communicating Sequential Processes, Prentice-Hall, 1985.
J.E. Hopcroft, J.D. Ullman, Introduction to Automata theory, Languages and Computation, Addison-Wesley, 1979.
F. Jahanian, A.K. Mok, “Safety analysis of timing properties in real-time systems,” IEEE Trans. on Software engineering, 12(9), 1986.
R. Koymans, “Specifying message passing and time-critical systems with temporal logic,” Ph.D. Thesis, Eindhoven Univ. of Tech., 1989.
H.R. Lewis, “Finite-state analysis of asynchronous circuits with bounded temporal uncertainty,” Tech. Report TR-15-89, Harvard Univ., 1989.
H.R. Lewis, “A logic of concrete time intervals,” 5th IEEE LICS, 1990.
R. McNaughton, “Testing and generating infinite sequences by a finite automaton,” Information and Control 9, 1966.
A. Pnueli, “Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends,” Current Trends in Concurrency, LNCS 244, Springer-Verlag, 1986.
G.M. Reed, A.W. Roscoe, “A timed model for communicating sequential processes,” 13th ICALP, LNCS 226, Springer-Verlag, 1986.
S. Safra, “On the complexity of ω-automata,” 29th IEEE FOCS, 1988.
A.P. Sistla, M.Y. Vardi, P. Wolper, “The complementation problem for Büchi automata with applications to temporal logic,” Theoretical Computer Science 49, 1987.
P. Wolper, M.Y. Vardi, A.P. Sistla, “Reasoning about infinite computation paths,” 24th IEEE FOCS, 1983.
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Alur, R., Dill, D. (1990). Automata for modeling real-time systems. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032042
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DOI: https://doi.org/10.1007/BFb0032042
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