Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

  • Blaise Genest
  • Hugo Gimbert
  • Anca Muscholl
  • Igor Walukiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6199)


Asynchronous automata are parallel compositions of finite-state 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.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Blaise Genest
    • 1
    • 2
  • Hugo Gimbert
    • 3
  • Anca Muscholl
    • 3
  • Igor Walukiewicz
    • 3
  1. 1.CNRS, IPAL UMI, joint with I2R-A*STAR-NUSSingapore
  2. 2.CNRS, IRISA UMR, joint with Université Rennes IFrance
  3. 3.LaBRI, CNRS/Université BordeauxFrance

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