Journal of Mathematical Sciences

, Volume 237, Issue 3, pp 432–444 | Cite as

The Structure of Isomorphisms of Universal Hypergraphical Automata

  • V. A. MolchanovEmail author


Universal hypergraphical automata are universally attracting objects in the category of automata for which the set of states and the set of output symbols are equipped with structures of hypergraphs. It was proved earlier that a wide class of such sort of automata are determined up to isomorphism by their semigroups of input symbols. We investigate the connection between isomorphisms of universal hypergraphical automata and isomorphisms of their components: semigroups of input symbols and hypergraphs of states and output symbols.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Berge, Graphs et hypergraphs, Dunod, Paris (1970).zbMATHGoogle Scholar
  2. 2.
    A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Amer. Math. Soc., Providence, Rhode Island (1964).Google Scholar
  3. 3.
    F. Karteszi, Introduction to Finite Geometries, North-Holland, Amsterdam (1976).zbMATHGoogle Scholar
  4. 4.
    A. V. Molchanov, “On definability of hypergraphs by their semigroups of homomorphisms,” Semigroup Forum, 62, No. 1, 53–65 (2001).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    V. A. Molchanov, “A universal planar automaton is determined by its semigroup of input symbols,” Semigroup Forum, 82, No. 1, 1–9 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    V. A. Molchanov, “Representation of universal planar automata by autonomous input signals,” Izv. Saratov. Univ., Ser. Mat. Mekh. Inform., 13, No. 2, Pt. 2, 31–37 (2013).Google Scholar
  7. 7.
    V. A. Molchanov, “Abstract characterization of semigroups of input signals of universal planar automata,” Izv. Saratov. Univ., Ser. Mat. Mekh. Inform., 15, No. 1, 113–121 (2015).CrossRefzbMATHGoogle Scholar
  8. 8.
    V. A. Molchanov, “Concrete characterization of universal planar automata,” J. Math. Sci., 206, No. 5, 554–560 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    B. I. Plotkin, L. Ja. Greenglaz, and A. A. Gvaramija, Algebraic Structures in Automata and Databases Theory, River Edge, Singapore; World Scientific, New York (1992).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Saratov State UniversitySaratovRussia

Personalised recommendations