Mediating for Reduction (on Minimizing Alternating Büchi Automata)

Authors Parosh A. Abdulla, Yu-Fang Chen, Lukas Holik, Tomas Vojnar



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Author Details

Parosh A. Abdulla
Yu-Fang Chen
Lukas Holik
Tomas Vojnar

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Parosh A. Abdulla, Yu-Fang Chen, Lukas Holik, and Tomas Vojnar. Mediating for Reduction (on Minimizing Alternating Büchi Automata). In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2302

Abstract

We propose a new approach for minimizing alternating B\"uchi automata (ABA). The approach is based on the so called \emph{mediated equivalence} on states of ABA, which is the maximal equivalence contained in the so called \emph{mediated preorder}. Two states $p$ and $q$ can be related by the mediated preorder if there is a~\emph{mediator} (mediating state) which forward simulates $p$ and backward simulates $q$. Under some further conditions, letting a computation on some word jump from $q$ to $p$ (due to they get collapsed) preserves the language as the automaton can anyway already accept the word without jumps by runs through the mediator. We further show how the mediated equivalence can be computed efficiently. Finally, we show that, compared to the standard forward simulation equivalence, the mediated equivalence can yield much more significant reductions when applied within the process of complementing B\"uchi automata where ABA are used as an intermediate model.
Keywords
  • Alternating Automata
  • Buchi Automata
  • Automata Minimization
  • Buchi Automata Complementation
  • Simulation Preorder
  • forward and backward simulation
  • mediated equivalence

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