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Deterministic representation of probabilistic systems by ergodic machines

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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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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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  • State Space
  • Random Number
  • Computational Mathematic
  • Number Generator
  • Probabilistic System