Universal Hypergraphic Automata Representation by Autonomous Input Symbols
Hypergraphic automata are automata with state sets and input symbol sets being hypergraphs which are invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are automata Atm(H1,H2). Here, H1 is a state hypergraph, H2 is classi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2018-10-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/757 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849401206811656192 |
|---|---|
| author | Ekaterina Khvorostukhina Vladimir Molchanov |
| author_facet | Ekaterina Khvorostukhina Vladimir Molchanov |
| author_sort | Ekaterina Khvorostukhina |
| collection | DOAJ |
| description | Hypergraphic automata are automata with state sets and input symbol sets being hypergraphs which are invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are automata Atm(H1,H2). Here, H1 is a state hypergraph, H2 is classified as an output symbol hypergraph, and S = EndH1 × Hom(H1,H2) is an input symbol semigroup. Such automata are called universal hypergraphic automata. The input symbol semigroup S of such an automaton Atm(H1,H2) is an algebra of mappings for such an automaton. Semigroup properties are interconnected with properties of the algebraic structure of the automaton. Thus, we can study universal hypergraphic automata with the help of their input symbol semigroups. In this paper, we investigated a representation problem of universal hypergraphic automata in their input symbol semigroup. The main result of the current study describes a universal hypergraphic automaton as a multiple-set algebraic structure canonically constructed from autonomous input automaton symbols. Such a structure is one of the major tools for proving relatively elementary definability of considered universal hypergraphic automata in a class of semigroups in order to analyze interrelation of elementary characteristics of universal hypergraphic automata and their input symbol semigroups. The main result of the paper is the solution of this problem for universal hypergraphic automata for effective hypergraphs with p-definable edges. It is an important class of automata because such an algebraic structure variety includes automata with state sets and output symbol sets represented by projective or affine planes, along with automata with state sets and output symbol sets divided into equivalence classes. The article is published in the authors' wording. |
| format | Article |
| id | doaj-art-2e89b819a8e94ad3822d9db0f22c9e32 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2018-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-2e89b819a8e94ad3822d9db0f22c9e322025-08-20T03:37:50ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172018-10-0125556157110.18255/1818-1015-2018-5-561-571528Universal Hypergraphic Automata Representation by Autonomous Input SymbolsEkaterina Khvorostukhina0Vladimir Molchanov1Yuri Gagarin State Technical University of Saratov.Saratov State University.Hypergraphic automata are automata with state sets and input symbol sets being hypergraphs which are invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are automata Atm(H1,H2). Here, H1 is a state hypergraph, H2 is classified as an output symbol hypergraph, and S = EndH1 × Hom(H1,H2) is an input symbol semigroup. Such automata are called universal hypergraphic automata. The input symbol semigroup S of such an automaton Atm(H1,H2) is an algebra of mappings for such an automaton. Semigroup properties are interconnected with properties of the algebraic structure of the automaton. Thus, we can study universal hypergraphic automata with the help of their input symbol semigroups. In this paper, we investigated a representation problem of universal hypergraphic automata in their input symbol semigroup. The main result of the current study describes a universal hypergraphic automaton as a multiple-set algebraic structure canonically constructed from autonomous input automaton symbols. Such a structure is one of the major tools for proving relatively elementary definability of considered universal hypergraphic automata in a class of semigroups in order to analyze interrelation of elementary characteristics of universal hypergraphic automata and their input symbol semigroups. The main result of the paper is the solution of this problem for universal hypergraphic automata for effective hypergraphs with p-definable edges. It is an important class of automata because such an algebraic structure variety includes automata with state sets and output symbol sets represented by projective or affine planes, along with automata with state sets and output symbol sets divided into equivalence classes. The article is published in the authors' wording.https://www.mais-journal.ru/jour/article/view/757automatonsemigrouphypergraphinput symbol |
| spellingShingle | Ekaterina Khvorostukhina Vladimir Molchanov Universal Hypergraphic Automata Representation by Autonomous Input Symbols Моделирование и анализ информационных систем automaton semigroup hypergraph input symbol |
| title | Universal Hypergraphic Automata Representation by Autonomous Input Symbols |
| title_full | Universal Hypergraphic Automata Representation by Autonomous Input Symbols |
| title_fullStr | Universal Hypergraphic Automata Representation by Autonomous Input Symbols |
| title_full_unstemmed | Universal Hypergraphic Automata Representation by Autonomous Input Symbols |
| title_short | Universal Hypergraphic Automata Representation by Autonomous Input Symbols |
| title_sort | universal hypergraphic automata representation by autonomous input symbols |
| topic | automaton semigroup hypergraph input symbol |
| url | https://www.mais-journal.ru/jour/article/view/757 |
| work_keys_str_mv | AT ekaterinakhvorostukhina universalhypergraphicautomatarepresentationbyautonomousinputsymbols AT vladimirmolchanov universalhypergraphicautomatarepresentationbyautonomousinputsymbols |