×

State hypergroups of automata. (English) Zbl 0870.20053

Summary: A functorial passage from the category of automata without outputs and their homomorphisms into the category of preordered hypergroups and strong homomorphisms based on the concept of inertial relation extended into a preordering of a state set is used for describing some basic properties of automata. Further, the relational hypergroup product is treated in connection with products of automata.

MSC:

20N20 Hypergroups
68Q70 Algebraic theory of languages and automata
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Bavel Z.: The source as a tool in automata. Inform. Control. 18 (1971), 140-155. · Zbl 0221.94079 · doi:10.1016/S0019-9958(71)90324-X
[2] Bavel Z., Grzymala-Busse J., Soo Hong K.: On the conectivity of the product of automata. Fundam. Informaticae 7, 2 (1984), 225-265.
[3] Birkhoff G., Lipson J. D.: Heterogeneous algebras. J. Combinatorial Theory 8 (1970), 115-133. · Zbl 0211.02003 · doi:10.1016/S0021-9800(70)80014-X
[4] Corsini P.: Prolegomena of Hypergoup Theory. Aviani Editore, Tricesimo, 1993. · Zbl 0785.20032
[5] Čech E.: Topological Spaces. (Revised by Zdeněk Frolík and Miroslav Katětov) Academia, Prague, 1966. · Zbl 0141.39401
[6] Chvalina J.: Commutative hypergroups in the sense of Marty and ordered sets. Gen. Alg. and Ordered Sets, Proc. Inter. Conf., Olomouc (1994), 19-30. · Zbl 0827.20085
[7] Chvalina J., Chvalinová L.: Betweenness, automata, and commutative hypergroups. (Czech). Interim Grant Report FS VUT Brno (1993), 1-18.
[8] Dörfler W.: Halbgruppen und Automaten. Rend. Sem. Mat. Univ. Padova 50 (1973), 1-18. · Zbl 0284.20069
[9] Dörfler W.: The cartesian composition of automata. Math. Systems theory 11 (1978), 239-257. · Zbl 0385.68055 · doi:10.1007/BF01768479
[10] Dresher M., Ore O.: Theory of multigroups. Amer. J. Math. 60 (1938), 705-733. · Zbl 0019.10701 · doi:10.2307/2371606
[11] Foldes S.: Lexicographic summs of ordered sets and hypergrupoids. Alg. Hyperstructures and Appl. (T. Vougiouklis, Proc. 4th Inter. Congress Xanthi, Greece 1990, World Scientific, Singapore 1991, 97-101.
[12] Gecseg F., Peak I.: Algebraic Theory of Automata. Akademiai Kiado, Budapest, 1972.
[13] Marty F.: Sur une generalisation de la notion de groupe. Huitieme congr. math. scand., Stockholm 1934, 45-49. · JFM 61.1014.03
[14] Massouros C. G.: Automata and hypermoduloids. Alg. Hyperstructures and Appl. (M. Stefanescu, Proc. 5th Inter. Congress Jasi 1993, Hadronic Press, Palm Harbor, U.S.A., 1994, 251-256. · Zbl 0841.68076
[15] Massouros C. G.: An automaton during its operation. Alg. Hyperstructures and Appl. (M. Stefanescu, Proc. 5th Inter. Congress Jasi 1993, Hadronic Press, Palm Harbor, U.S.A., 1994, 267-276. · Zbl 0841.68077
[16] Massouros C. G., Mittas J.: Languages- automata and hypercompositional structures. Alg. Hyperstructures and Appl. (T. Vougiouklis, Proc. 4th Inter. Congress Xanthi, Greece 1990, World Scientific, Singapore 1991, 137-147. · Zbl 0745.20062
[17] Massouros C. G.: Hypercompositional structures in the theory of the languages and automata. Anal.stiinfice Ale Univ. ”Al. I, Cuza” Iasi III, Informatica 1994, 65-73. · Zbl 0840.68066
[18] Prenowitz W., Jantosciak J.: Geometries and join spaces. Journ. reine angew. Math. 257 (1972), 100-128. · Zbl 0264.50002
[19] Shukla W., Srivastava A. K.: A topology for automata. A Note. Inform. Control 32 (1976), 163-168. · Zbl 0338.94028 · doi:10.1016/S0019-9958(76)90206-0
[20] Vougiouklis T.: Cyclicity in a special class of hypergroups. Acta Univ. Carol. Math. Phys. 22, 1 (1981), 3-6. · Zbl 0495.20042
[21] Vougiouklis T.: Generalization of P-hypergroups. Rend. Circ. Mat. Palermo. Ser. 2 36 (1988), 114-121. · Zbl 0652.20069 · doi:10.1007/BF02844705
[22] Vougiouklis T. (ed.): Algebraic Hyperstructures and Applications. Proc. Fourth. Internal Congress, Xanthi, Greece 1990, World Sci. Singapore-New Jersey-London-Hong Kong, 1991.
[23] Warner M. W.: Semigroup, group quotient and homogeneous automata. Inform. Control 47 (1980), 59-66. · Zbl 0474.68069 · doi:10.1016/S0019-9958(80)90277-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.