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Yet another proof of the cascade decomposition theorem for finite automata

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Abstract

We give here a short proof that each finite automaton can be built as a cascade of permutation automata and identity-reset automata.

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References

  1. K. Krohn andJ. Rhodes, Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines.Trans. Amer. Math. Soc. 116 (1965), 450–464.

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  2. J. Hartmanis andR. E. Stearns,Algebraic Structure Theory of Sequential Machines, Prentice Hall, 1966.

  3. A. H. Clifford andG. B. Preston,The Algebraic Theory of Semigroups, Amer. Math. Soc. Math. Surveys No. 7, Providence, R.I., 1961.

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Authors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Paul Zeiger

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  1. Paul Zeiger
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Zeiger, P. Yet another proof of the cascade decomposition theorem for finite automata. Math. Systems Theory 1, 225–228 (1967). https://doi.org/10.1007/BF01703821

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  • DOI: https://doi.org/10.1007/BF01703821

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