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A decomposition theorem for probabilistic transition systems

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Book cover STACS 93 (STACS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

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Abstract

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.

The results presented in this paper have been obtained while the author was with INRIA/IRISA, Rennes, France.

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References

  1. M.A. Arbib, Theories of Abstract Automata, Prentice-Hall, Englewood Cliffs, 1968.

    Google Scholar 

  2. S. Eilenberg, Automata, Languages and Machines, Vol. B, Academic Press, New York, 1976.

    Google Scholar 

  3. A. Ginzburg, Algebraic Theory of Automata, Academic Press, New York, 1968.

    Google Scholar 

  4. J.G. Kemeny and J.L. Snell, Finite Markov Chains, Van Nostrand, New York, 1960.

    Google Scholar 

  5. K. Krohn and J.L. Rhodes, Algebraic Theory of Machines, I Principles of Finite Semigroups and Machines, Transactions of the American Mathematical Society 116, 450–464, 1965.

    Google Scholar 

  6. G. Lallement, Semigroups and Combinatorial Applications, Wiley, New York, 1979.

    Google Scholar 

  7. O. Maler and A. Pnueli, Tight Bounds on the Complexity of Cascaded Decomposition of Automata, Proc. 31st FOCS, 672–682, 1990.

    Google Scholar 

  8. A. Paz, Introduction to Probabilistic Automata, Academic Press, New York, 1970.

    Google Scholar 

  9. J.-E. Pin, Varieties of Formal Languages, Plenum, New York, 1986.

    Google Scholar 

  10. P.H. Starke, Abstract Automata, North-Holland, Amsterdam, 1972.

    Google Scholar 

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Authors and Affiliations

  1. LGI-IMAG (Campus), B.P. 53x, 38041, Grenoble, France

    Oded Maler

Authors
  1. Oded Maler
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P. Enjalbert A. Finkel K. W. Wagner

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© 1993 Springer-Verlag Berlin Heidelberg

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Maler, O. (1993). A decomposition theorem for probabilistic transition systems. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_33

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  • DOI: https://doi.org/10.1007/3-540-56503-5_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

  • eBook Packages: Springer Book Archive

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