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Observability and Nerode equivalence in concrete categories

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Fundamentals of Computation Theory (FCT 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 117))

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Abstract

Functorial automata are studied in a concrete category K with structured hom-sets. For each functor F : K → K, which respects this structure, the observability morphisms of F-automata are defined analogously to those of sequential automata. If each F-automaton has an observable reduction, the minimization problem is both much simplified (in fact, translated to the image factorization of the observability morphisms) and made global. We prove that this is the case iff each behavior has a Nerode equivalence. First, we present a survey of the related results on minimal realization and Nerode equivalence.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Technical University Prague, Czechoslovakia

    J. Adámek

Authors
  1. J. Adámek
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Editor information

Ferenc Gécseg

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© 1981 Springer-Verlag Berlin Heidelberg

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Adámek, J. (1981). Observability and Nerode equivalence in concrete categories. In: Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1981. Lecture Notes in Computer Science, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10854-8_1

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  • DOI: https://doi.org/10.1007/3-540-10854-8_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10854-2

  • Online ISBN: 978-3-540-38765-7

  • eBook Packages: Springer Book Archive

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