Representing Periodic Temporal Information with Automata
Pierre Wolper
Universit´e de Li`ege
Institut Montefiore, B28,
4000 Li`ege, Belgium
E-mail: [email protected]
Abstract
Motivated by issues in temporal databases and in the verification of infinite-state systems, this talk considers the problem of representing periodic dense time information. Doing so requires handling a theory that combines discrete and continuous variables, since discrete variables are es-sential for representing periodicity. An automata-based ap-proach for dealing with such a combined theory is thus in-troduced.
This approach uses the fact that real numbers can be rep-resented by infinite sequences of digits and hence that sets of real numbers can be viewed as infinite-word languages, which can be recognized by infinite-word finite automata. Since these automata can represent all linear constraints, can express intergerhood, and are closed under the first-order constructs, the presented approach can handle the full first-order theory of linear constraints over the reals and in-tegers.
One problem with using infinite-word automata is that the algorithms for complementing them are especially com-plicated and difficult to implement effectively. Fortunately, with the help of topological arguments it can be shown that a very restricted and much more tractable class of infinite-word automata are sufficient for the purpose on hand.
Background information on the topics presented in this talk can be found in [1, 2, 3, 4].
References
[1] B. Boigelot, S. Jodogne, and P. Wolper. On the use of weak automata for deciding linear arithmetic with integer and real variables. In Proc. International Joint Conference on Auto-mated Reasoning (IJCAR), Lecture Notes in Computer Sci-ence, Siena, June 2001. Springer-Verlag. to appear.
[2] B. Boigelot, S. Rassart, and P. Wolper. On the expressiveness of real and integer arithmetic automata. In Proc. 25th Col-loq. on Automata, Programming, and Languages (ICALP),
volume 1443 of Lecture Notes in Computer Science, pages 152–163. Springer-Verlag, July 1998.
[3] P. Wolper. Linear repeating points. In G. Kuper, L. Libkin, and J. Paredaens, editors, Constraint Databases, chapter 13, pages 305–314. Springer-Verlag, 2000.
[4] P. Wolper and B. Boigelot. On the construction of automata from linear arithmetic constraints. In Proc. 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, volume 1785 of Lecture Notes in Com-puter Science, pages 1–19, Berlin, March 2000. Springer-Verlag.
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Proceedings of the Eighth International Symposium on Temporal Representation and Reasoning (TIME’01) 1530-1311/01 $10.00 © 2001 IEEE
