Abstract characterization of semigroups of input signals of universal planar automata
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 113-121.

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Universal planar automata are universally attracted objects in the category of automata, for which sets of states and output signals are endowed with structures of planes. The main results of the paper give us necessary and sufficient conditions under which an arbitrary automaton is isomorphic to a universal planar automaton and an arbitrary semigroup is isomorphic to the semigroup of input signals of a universal planar automata.
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V. A. Molchanov. Abstract characterization of semigroups of input signals of universal planar automata. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 113-121. http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a15/

[1] Karteszi F., Introduction to finite geometries, North-Holland, Amsterdam, 1976, 266 pp.

[2] Plotkin B. I., Greenglaz L. Ja., Gvaramija A. A., Algebraic structures in automata and databases theory, World Scientific, Singapore–River Edge, 1992

[3] Ulam S. M., A Collection of Mathematical Problems, Interscience Publishers, New York, 1960, 150 pp.

[4] Jonson B., Topics in Universal Algebras, Lecture Notes in Mathematics, 250, Springer-Verlag, Berlin–N. Y., 1972, 220 pp. | DOI

[5] Molchanov V. A., “A universal planar automaton is determined by its semigroup of input symbols”, Semigroup Forum, 82 (2011), 1–9 | DOI

[6] Molchanov V. A., “Concrete characterization of universal planar automata”, Fundamentalnaya i prikladnaya matematika, 18:3 (2013), 139–148 (in Russian)

[7] Birkhoff G., Lipson J. D., “Heterogeneous Algebras”, J. Combinatorial Theory, 8 (1970), 115–133 | DOI

[8] Ershov Yu. L., Palyutin E. A., Mathematical Logic, Mir Publishers, M., 1984, 303 pp.

[9] Molchanov V. A., “Representation of Universal Planar Automata by Autonomous Input Signals”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 13:2(2) (2013), 31–37 (in Russian)