Observability and Nerode equivalence in concrete categories

  • J. Adámek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 117)


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.


Free Algebra Minimal Reduction Minimal Realization Concrete Category Pointwise Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    J. Adámek: Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae 15(1974), 589–602.Google Scholar
  2. [2]
    J. Adámek: Cogeneration of algebras in regular categories. Bull. Austral. Math. Soc. 15 (1976), 55–64.Google Scholar
  3. [3]
    J. Adámek: Realization theory for automata in categories. J.Pure Appl. Algebra 9 (1977), 281–296.Google Scholar
  4. [4]
    J. Adámek: Categorical realization theory II: Nerode equivalences. Algebraische Modelle, Kategorien und Gruppoide (H.-J. Hoehnke ed.), Akademie-Verlag, Berlin 1979.Google Scholar
  5. [5]
    J. Adámek, H. Ehrig, V. Trnková: An equivalence of system-theoretical and categorical notions. Kybernetika 16 (1980)Google Scholar
  6. [6]
    M.A. Arbib, E.G. Manes: Machines in a category — an expository introduction. Lect. Notes Comp. Sci. 25, Springer-Verlag 1975.Google Scholar
  7. [7]
    M.A. Arbib, E.G. Manes: Adjoint machines, state-behavior machines and duality. J. Pure Appl. Algebra 6 (1975), 313–344.Google Scholar
  8. [8]
    B. Banaschewski, E. Nelson: Tensor products and bimorphisms. Canad. Math. Bull. 19 (1976), 385–402.Google Scholar
  9. [9]
    V. Trnková: Automata and categories. Lect.N. Comp. Sci. 32, Springer-Verlag 1975, 138–152.Google Scholar
  10. [10]
    V. Trnková, J. Adámek: Realization is not universal. Preprint, Heft 21, Weiterbildungszentrum TU Dresden (1977), 38–55.Google Scholar
  11. [11]
    V. Trnková, J. Adámek, V. Koubek, J. Reiterman: Free algebras, input processes and free monads. Comment. Math. Univ. Carolinae 16 (1975), 339–351.Google Scholar
  12. [12]
    V. Trnková: On minimal realizations of behavior maps in categorial automata theory. Comment. Math. Univ. Carolinae 15 (1974), 555–566.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Adámek
    • 1
  1. 1.Faculty of Electrical EngineeringTechnical University PragueCzechoslovakia

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