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Undecidability of Universality for Timed Automata with Minimal Resources

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Formal Modeling and Analysis of Timed Systems (FORMATS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4763))

Abstract

Timed automata were introduced by Alur and Dill in the early 1990s and have since become the most prominent modelling formalism for real-time systems. A fundamental limit to the algorithmic analysis of timed automata, however, results from the undecidability of the universality problem: does a given timed automaton accept every timed word? As a result, much research has focussed on attempting to circumvent this difficulty, often by restricting the class of automata under consideration, or by altering their semantics.

In this paper, we study the decidability of universality for classes of timed automata with minimal resources. More precisely, we consider restrictions on the number of states and clock constants, as well as the size of the event alphabet. Our main result is that universality remains undecidable for timed automata with a single state, over a single-event alphabet, and using no more than three distinct clock constants.

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Authors and Affiliations

  1. Oxford University Computing Laboratory,  

    Sara Adams, Joël Ouaknine & James Worrell

Authors
  1. Sara Adams
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  2. Joël Ouaknine
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  3. James Worrell
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Editor information

Jean-François Raskin P. S. Thiagarajan

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Adams, S., Ouaknine, J., Worrell, J. (2007). Undecidability of Universality for Timed Automata with Minimal Resources. In: Raskin, JF., Thiagarajan, P.S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2007. Lecture Notes in Computer Science, vol 4763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75454-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-75454-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75453-4

  • Online ISBN: 978-3-540-75454-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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