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A Myhill-Nerode Style Characterization for Timed Automata with Integer Resets

Authors Kyveli Doveri , Pierre Ganty , B. Srivathsan

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Author Details

Kyveli Doveri
  • University of Warsaw, Poland
Pierre Ganty
  • IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain
B. Srivathsan
  • Chennai Mathematical Institute, India
  • CNRS IRL 2000, ReLaX, Chennai, India

Funding

  • Doveri, Kyveli: Supported by the ERC grant INFSYS, agreement no. 950398. Results partly obtained when previously affiliated with the IMDEA Software Institute.
  • Ganty, Pierre: This publication is part of the grant PID2022-138072OB-I00, funded by MCIN/AEI/10.13039/501100011033/FEDER, UE.

Cite As Get BibTex

Kyveli Doveri, Pierre Ganty, and B. Srivathsan. A Myhill-Nerode Style Characterization for Timed Automata with Integer Resets. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.21

Abstract

The well-known Nerode equivalence for finite words plays a fundamental role in our understanding of the class of regular languages. The equivalence leads to the Myhill-Nerode theorem and a canonical automaton, which in turn, is the basis of several automata learning algorithms. A Nerode-like equivalence has been studied for various classes of timed languages.
In this work, we focus on timed automata with integer resets. This class is known to have good automata-theoretic properties and is also useful for practical modeling. Our main contribution is a Nerode-style equivalence for this class that depends on a constant K. We show that the equivalence leads to a Myhill-Nerode theorem and a canonical one-clock integer-reset timed automaton with maximum constant K. Based on the canonical form, we develop an Angluin-style active learning algorithm whose query complexity is polynomial in the size of the canonical form.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Timed languages
  • Timed automata
  • Canonical representation
  • Myhill-Nerode equivalence
  • Integer reset

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