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Mathematical systems theory

, Volume 11, Issue 1, pp 239–257 | Cite as

The cartesian composition of automata

  • Willibald Dörfler
Article

Abstract

There are several known ways to define a product automaton on the cartesian product of the state sets of two given automata. This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties of the factors. A main result is that any finite connected automaton has a unique representation as a cartesian composition of prime automata.

Keywords

Computational Mathematic Unique Representation Product Automaton Connected Automaton 
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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References

  1. 1.
    G. Birkhoff, andJ. D. Lipson, Heterogeneous algebras,J. Combinatorial Theory 8 (1970), 115–133.Google Scholar
  2. 2.
    W. Dörfler, Zur algebraischen Theorie der Automaten.EIK 9 (1973), 171–177.Google Scholar
  3. 3.
    W. Dörfler, Halbgruppen und Automaten,Rend. Sem. Mat. Univ. Padova 50 (1973), 1–18.Google Scholar
  4. 4.
    S. Eilenberg, Automata, Languages and Machines, Academic Press, 1974.Google Scholar
  5. 5.
    A. C. Fleck, Isomorphism groups of automata,J. Assoc. Comp. Machinery 9 (1962), 469–476.Google Scholar
  6. 6.
    A. C. Fleck, On the automorphism group of an automaton,J. Assoc. Comp. Machinery 12 (1965), 566–569.Google Scholar
  7. 7.
    F. Gecseg andI. Peak,Algebraic Theory of Automata, Akadémiai Kiado, Budapest, 1972.Google Scholar
  8. 8.
    H. E. Pickett, Note concerning the algebraic theory of automata,J. Assoc. Comp. Mackinery 14 (1967), 282–288.Google Scholar
  9. 9.
    Ch. A. Trauth, Group-type automata,J. Assoc. Comp. Machinery 13 (1966), 160–175.Google Scholar
  10. 10.
    G. P. Weeg, The structure of an automaton and its operation preserving group,J. Assoc. Comp. Machinery 9 (1962), 345–349.Google Scholar
  11. 11.
    G. P. Weeg, The automorphism group of the direct product of strongly related automata,J. Assoc. Comp. Machinery 12 (1965), 187–195.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1978

Authors and Affiliations

  • Willibald Dörfler
    • 1
  1. 1.Universität für BildungswissenschaftenKlagenfurtAustria

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