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Deterministic representation of probabilistic systems by ergodic machines

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Abstract

Homomorphic simplification is one way of defining valid simplication of deterministic models. To allow the use of similar techniques for probabilistic systems, we introduce the concept of an ergodic machine. An ergodic machine is a specification for a deterministic system and it represents and associated probabilistic system when viewed properly. The probabilistic features arise by using an ergodic transformation on a “hidden” partial state space. An ergodic transformation can be thought of as an ideal random number generator. In this paper, we develop the concepts of ergodic machines necessary for faithfully representing probabilistic systems and make connections to markov chains and pseudo random number generators.

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Authors and Affiliations

  1. Department of Computer Science, University of Oregon, 97405, Eugene, Oregon, USA

    Sudhir Aggarwal

  2. Lawrence Livermore Laboratory, University of California, 94550, Livermore, California, USA

    Sudhir Aggarwal

Authors
  1. Sudhir Aggarwal
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Additional information

This research represents a portion of the author's Ph.D. dissertation at the University of Michigan under the supervision of Prof. Bernard Zeigler. The work was partially supported by NSF Grant DCR71-01997 and the U.S. Energy Research and Development Administration, contract No. W-7405-Eng-48.

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Aggarwal, S. Deterministic representation of probabilistic systems by ergodic machines. Math. Systems Theory 10, 345–361 (1976). https://doi.org/10.1007/BF01683284

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  • DOI: https://doi.org/10.1007/BF01683284

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