A decomposition theorem for probabilistic transition systems

  • Oded Maler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


In this paper we prove that every finite Markov chain can be decomposed into a cascade product of a Bernoulli process and several simple permutation-reset deterministic automata. The original chain is a statehomomorphic image of the product. By doing so we give a positive answer to an open question stated in [Paz71] concerning the decomposability of probabilistic systems. Our result is based on the surprisingly-original observation that in probabilistic transition systems, “randomness” and “memory” can be separated in such a way that allows the non-random part to be treated using common deterministic automata-theoretic techniques. The same separation technique can be applied as well to other kinds of non-determinism.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Oded Maler
    • 1
  1. 1.LGI-IMAG (Campus)GrenobleFrance

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