Optimal Zielonka-type construction of deterministic asynchronous automata

  • Authors:
  • Blaise Genest;Hugo Gimbert;Anca Muscholl;Igor Walukiewicz

  • Affiliations:
  • CNRS, IPAL, UMI, I2R-A*STAR, NUS, Singapore and CNRS, IRISA, UMR, Université Rennes I, France;LaBRI, CNRS, Université Bordeaux, France;LaBRI, CNRS, Université Bordeaux, France;LaBRI, CNRS, Université Bordeaux, France

  • Venue:
  • ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
  • Year:
  • 2010

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Abstract

Asynchronous automata are parallel compositions of finitestate processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be represented by a deterministic asynchronous automaton. In this paper we improve the construction, in that the size of the obtained asynchronous automaton is polynomial in the size of a given DFA and simply exponential in the number of processes. We show that our construction is optimal within the class of automata produced by Zielonka-type constructions. In particular, we provide the first non trivial lower bound on the size of asynchronous automata.