Cite this article as:
Molchanov V. A. Representation of universal planar automata by autonomous input signals . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 31-37. DOI: https://doi.org/10.18500/1816-9791-2013-13-2-2-31-37
Representation of universal planar automata by autonomous input signals
Universal planar automata are universally attracted objects in the category of automata, whose sets of states and output signals are endowed with structures of planes. The main result of the paper shows that any universal planar automaton is isomorphic to a many-sorted algebraic system canonically constructed from autonomous input signals of the automaton.
1. Plotkin B. I., Greenglaz L. Ja., Gvaramija A. A.
Algebraic structures in automata and databases theory.
Singapore, River Edge, NJ, World Scientific, 1992. (Rus.
ed.: Plotkin B. I., Gringlaz L. Ia., Gvaramiia A. A.
Elementy algebraicheskoi teorii avtomatov. Moscow,
Vysshaia shkola, 1994, 192 p.)
2. Simovici Dan A. On the theory of reduction of semilatticial
automata. An. Sti. ale Univ. «Al. l. Cuza» Din
Iasi. (Ser. Nou˘a). Sec. 1a., 1976, vol. 22, no. 1, pp. 107–
110.
3. G´ecseg F. O proizvedeniiakh uporiadochennykh
avtomatov. I [On products of ordered automata. I]. Acta
Sci. Math., 1963, vol. 24, no. 3–4, pp. 244–250 (in
Russian).
4. G´ecseg F. O proizvedeniah uporadochennyh
avtomatov. II [On products of ordered automata. II].
Acta Sci. Math., 1964, vol. 25, no. 1–2, pp. 124–128 (in
Russian).
5. Eilenberg S. Automata, languages and machines.
Vol. B. New York, San Francisco, London, Academic
Press, 1976, 451 p.
6. Introduction to finite geometries. Amsterdam, North-
Holland Publishing Co., 1976. (Russ. ed.: Kartesi F.
Vvedenie v konechnye geometrii. Moscow, Nauka, 1980,
320 p.)
7. Ulam S. M. A Collection of Mathematical Problems.
New Mexico, Los Alamos Scientific Laboratories, 1960.
(Rus. ed.: Ulam S. Nereshennye matematicheskie
zadachi. Moscow, Nauka, 1964, 168 p.)
8. Gluskin L. M. Polugruppy i kol’tsa endomorfizmov
lineinykh prostranstv [Semigroups and rings of
endomorphisms of linear spaces]. Izv. Akad. Nauk SSSR
Ser. Mat., 1959, vol. 23, pp. 841–870 (in Russian).
9. Jonson B. Topics in Universal Algebras. Lecture Notes
in Mathematics. Berlin, Heidelberg, New York, Springer
Verlag, 1972, 220 p.
10. Konig D. Theorie der endlichen und unendlichen
Graphen. Leipzig, Acad. Verlag M.B.H., 1936, 258 p.
11. Krasner M. Endotheorie de Galois abstraita. Semin.
Dubriel, Dubriel-Jacotin, Lesieur et Pisot. Fac. sci.
Paris, 1968–1969(1970), vol. 22, no 1, pp. 6/01-6/19.
12. Molchanov V. A. A universal planar automaton is
determined by its semigroup of input symbols. Semigroup
Forum, 2011, vol. 82, pp. 1–9.
13. Molchanov V. A. Konkretnaia kharakteristika
universal’nykh planarnykh avtomatov [On concrete
characterization of universal planar automata].
Matematika. Mehanika [Mathematics. Mechanics].
Saratov, Saratov Univ. Press, 2011, iss. 13, pp. 67–69
(in Russian).
14. Molchanov V. A. On relatively elementary definability
of the class of universal planar automata in the class
of all semigroups. Algebra i matematicheskaia logika :
tez. dokl. Mezhdunar. konf., posviashch. 100-letiiu
so dnia rozhdeniia V. V. Morozova [Proc. of the
international conference dedicated to 100-th anniversary
of V. V. Morozov and youth school-conf. «Modern
Problems of Algebra & Mathematical Logic»]. Kazan,
2011, pp. 145–147 (in Russian).
15. Ershov Yu. L. Problemy razreshimosti i konstruktivnye
modeli [Problems of decidability and constructive
models]. Moscow, Nauka, 1980, 416 p. (in Russian).
