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An algebraic theory of real-time formal languages

Abstract : A timed automaton is an automaton augmented with several clocks that measure the time passage and may influence state changes in the system. Timed automata were introduced as a formal model for real-time systems hoping that their role in the verification of such systems will be similar to the role of finite automata in the systematic search of errors in the design of untimed systems. In our thesis we are concerned with several theoretical questions related to timed automata and timed languages. In the first part of the thesis we investigate a simple sub-class of timed automata with one clock which is reset at each transition. We show that for this sub-class we can obtain simple analogs of the classical results of automata theory, namely Kleene and Myhill-Nerode theorems and closure under complementation. The second and main part of the thesis is motivated by the timed regular expressions of Asarin, Caspi and Maler where it was shown that, in order to match the expressive power of timed automata, one needs to introduce intersection into the expressions. We investigate an alternative to intersection by using colored parentheses for defining timing restrictions on overlapping parts of a sequence. This idea leads to an alternative representation of languages of timed automata, which is based on a new class of languages called here . We develop the theory of regular expressions over regminoes and prove that their emptiness problem is undecidable in general, and decidable for a large subclass of languages. From these results we develop new data-structures and algorithms for solving emptiness and reachability problems for timed automata and regular expressions.
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Contributor : Thèses Imag <>
Submitted on : Monday, February 16, 2004 - 10:48:18 AM
Last modification on : Thursday, November 19, 2020 - 3:58:01 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:18:28 PM


  • HAL Id : tel-00004672, version 1



Catalin Dima. An algebraic theory of real-time formal languages. Modeling and Simulation. Université Joseph-Fourier - Grenoble I, 2001. English. ⟨tel-00004672⟩



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