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Timed regular expressions
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Source Journal of the ACM (JACM) archive
Volume 49 ,  Issue 2  (March 2002) table of contents
Pages: 172 - 206  
Year of Publication: 2002
ISSN:0004-5411
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 13,   Downloads (12 Months): 80,   Citation Count: 6
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ABSTRACT

In this article, we define timed regular expressions, a formalism for specifying discrete behaviors augmented with timing information, and prove that its expressive power is equivalent to the timed automata of Alur and Dill. This result is the timed analogue of Kleene Theorem and, similarly to that result, the hard part in the proof is the translation from automata to expressions. This result is extended from finite to infinite (in the sense of Büchi) behaviors. In addition to these fundamental results, we give a clean algebraic framework for two commonly accepted formalisms for timed behaviors, time-event sequences and piecewise-constant signals.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
Rajeev Alur , David L. Dill, A theory of timed automata, Theoretical Computer Science, v.126 n.2, p.183-235, April 25, 1994  [doi>10.1016/0304-3975(94)90010-8 ]
 
2
Arden, D. 1960. Delayed-logic and finite-state machines. In Theory of Computing Machine Design. Univ. of Michigan Press, pp. 1--35.
 
3
Eugene Asarin, Equations on Timed Languages, Proceedings of the First International Workshop on Hybrid Systems: Computation and Control, p.1-12, April 13-15, 1998
 
4
E. Asarin , P. Caspi , O. Maler, A Kleene theorem for timed automata, Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, p.160, June 29-July 02, 1997
 
5
Patricia Bouyer , Antoine Petit, Decomposition and Composition of Timed Automata, Proceedings of the 26th International Colloquium on Automata, Languages and Programming, p.210-219, July 11-15, 1999
 
6
Patricia Bouyer , Antoine Petit, A Kleene/Büchi-like theorem for clock languages, Journal of Automata, Languages and Combinatorics, v.7 n.2, p.167-186, November 2001
 
7
Büchi, J. 1960. A decision method in restricted second order arithmetic. In Proceedings of the International Congress on Logic, Methodology and Philosophy of Science, E. Nagel, Ed. Stanford University Press, Stanford, Calif.
 
8
Conway, J. H. 1971. Regular Algebra and Finite Machines, Chapman & Hall, London, England.
 
9
Cătălin Dima, Real-time automata, Journal of Automata, Languages and Combinatorics, v.6 n.1, p.3-23, Jan. 2001
 
10
Philippe Herrmann, Renaming is Necessary in Timed Regular Expressions, Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science, p.47-59, December 13-15, 1999
 
11
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13
Li Xuandong , Zheng Tao , Hou Jianmin , Zhao Jianhua , Zheng Guoliang, Hybrid Regular Expressions, Proceedings of the First International Workshop on Hybrid Systems: Computation and Control, p.384-399, April 13-15, 1998
 
14
Oded Maler , Zohar Manna , Amir Pnueli, From Timed to Hybrid Systems, Proceedings of the Real-Time: Theory in Practice, REX Workshop, p.447-484, June 03-07, 1991
 
15
McNaughton, R. 1966. Testing and generating infinite sequences by a finite automaton. Inf. Contr. 9, 521--530.
 
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McNaughton, R., and Yamada, H. 1960. Regular expressions and state graphs for automata. IRE Trans. Elect. Comput. EC-9, 39--47.
 
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Alexander Moshe Rabinovich , Boris A. Trakhtenbrot, From Finite Automata toward Hybrid Systems (Extended Abstract), Proceedings of the 11th International Symposium on Fundamentals of Computation Theory, p.411-422, September 01-03, 1997
 
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Wolfgang Thomas, Automata on infinite objects, Handbook of theoretical computer science (vol. B): formal models and semantics, MIT Press, Cambridge, MA, 1991
 
19
Boris Trakhtenbrot, Origins and Metamorphoses of The Trinity: Logic, Nets, Automata, Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, p.506, June 26-29, 1995
 
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CITED BY  6
 
Jérôme Durand-Lose, A Kleene theorem for splitable signals, Information Processing Letters, v.89 n.5, p.237-245, 16 March 2004
Ramzi Ben Salah , Marius Bozga , Oded Maler, On timed components and their abstraction, Proceedings of the 2007 conference on Specification and verification of component-based systems: 6th Joint Meeting of the European Conference on Software Engineering and the ACM SIGSOFT Symposium on the Foundations of Software Engineering, p.63-71, September 03-04, 2007, Dubrovnik, Croatia
 
Paulo Tabuada , George J. Pappas , Pedro Lima, Compositional Abstractions of Hybrid Control Systems, Discrete Event Dynamic Systems, v.14 n.2, p.203-238, April 2004
 
Patricia Bouyer , Antoine Petit , Denis Thérien, An algebraic approach to data languages and timed languages, Information and Computation, v.182 n.2, p.137-162, 01 May 2003
 
Patricia Bouyer, A logical characterization of data languages, Information Processing Letters, v.84 n.2, p.75-85, 31 October 2002
 
Béatrice Bérard , Paul Gastin , Antoine Petit, Timed substitutions for regular signal-event languages, Formal Methods in System Design, v.31 n.2, p.101-134, October 2007

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS
      Subjects: Real-time and embedded systems

  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.3 Formal Languages
          Subjects: Classes defined by grammars or automata (e.g., context-free languages, regular sets, recursive sets)

Additional Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.3 Formal Languages
          Subjects: Classes defined by grammars or automata (e.g., context-free languages, regular sets, recursive sets); Algebraic language theory


General Terms:
Languages, Theory


Keywords:
Kleene theorem, timed automata, timed languages


REVIEW

"Jari Ojala : Reviewer"

Classical automata theory deals with discrete event sequences, and the notion of time is not included in the algebraic formulation of the automata theory. The authors of this paper create an algebraic framework similar to the classical automata th  more...


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