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Dynamic Data Structures for Timed Automata Acceptance

Authors Alejandro Grez, Filip Mazowiecki, Michał Pilipczuk, Gabriele Puppis, Cristian Riveros



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Author Details

Alejandro Grez
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile
Filip Mazowiecki
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
Michał Pilipczuk
  • University of Warsaw, Poland
Gabriele Puppis
  • University of Udine, Italy
Cristian Riveros
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile

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Alejandro Grez, Filip Mazowiecki, Michał Pilipczuk, Gabriele Puppis, and Cristian Riveros. Dynamic Data Structures for Timed Automata Acceptance. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.IPEC.2021.20

Abstract

We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so through the lenses of parameterized dynamic data structures: we assume that the automaton is fixed and its size is the parameter, while the input word is revealed as in a stream, one symbol at a time following the natural order on positions. The goal is to design a dynamic data structure that can be efficiently updated upon revealing the next symbol, while maintaining the answer to the query on whether the word consisting of symbols revealed so far is accepted by the automaton. We provide complexity bounds for this dynamic acceptance problem for timed automata that process symbols interleaved with time spans. The main contribution is a dynamic data structure that maintains acceptance of a fixed one-clock timed automaton 𝒜 with amortized update time 2^{𝒪(|𝒜|)} per input symbol.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • timed automata
  • data stream
  • dynamic data structure

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