Multi-solid varieties and Mh-transducers
We consider the concepts of colored terms and multi-hypersubstitutions. If t∈Wτ(X) is a term of type τ, then any mapping αt:PosF(t)→N of the non-variable positions of a term into the set of natural numbers is called a coloration of t. The set Wcτ(X) of colored terms consists of all pairs ⟨t,αt⟩....
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| Дата: | 2007 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152366 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Multi-solid varieties and Mh-transducers / S. Shtrakov // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 113–131. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1523662019-06-11T01:25:24Z Multi-solid varieties and Mh-transducers Shtrakov, S. We consider the concepts of colored terms and multi-hypersubstitutions. If t∈Wτ(X) is a term of type τ, then any mapping αt:PosF(t)→N of the non-variable positions of a term into the set of natural numbers is called a coloration of t. The set Wcτ(X) of colored terms consists of all pairs ⟨t,αt⟩. Hypersubstitutions are maps which assign to each operation symbol a term with the same arity. If M is a monoid of hypersubstitutions then any sequence ρ=(σ1,σ2,…) is a mapping ρ:N→M, called a multi-hypersubstitution over M. An identity t≈s, satisfied in a variety V is an M-multi-hyperidentity if its images ρ[t≈s] are also satisfied in V for all ρ∈M. A variety V is M-multi-solid, if all its identities are M−multi-hyperidentities. We prove a series of inclusions and equations concerning M-multi-solid varieties. Finally we give an automata realization of multi-hypersubstitutions and colored terms. 2007 Article Multi-solid varieties and Mh-transducers / S. Shtrakov // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 113–131. — Бібліогр.: 10 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:08B15, 03C05, 08A70. http://dspace.nbuv.gov.ua/handle/123456789/152366 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider the concepts of colored terms and multi-hypersubstitutions. If t∈Wτ(X) is a term of type τ, then any mapping αt:PosF(t)→N of the non-variable positions of a term into the set of natural numbers is called a coloration of t. The set Wcτ(X) of colored terms consists of all pairs ⟨t,αt⟩. Hypersubstitutions are maps which assign to each operation symbol a term with the same arity. If M is a monoid of hypersubstitutions then any sequence ρ=(σ1,σ2,…) is a mapping ρ:N→M, called a multi-hypersubstitution over M. An identity t≈s, satisfied in a variety V is an M-multi-hyperidentity if its images ρ[t≈s] are also satisfied in V for all ρ∈M. A variety V is M-multi-solid, if all its identities are M−multi-hyperidentities. We prove a series of inclusions and equations concerning M-multi-solid varieties. Finally we give an automata realization of multi-hypersubstitutions and colored terms. |
| format |
Article |
| author |
Shtrakov, S. |
| spellingShingle |
Shtrakov, S. Multi-solid varieties and Mh-transducers Algebra and Discrete Mathematics |
| author_facet |
Shtrakov, S. |
| author_sort |
Shtrakov, S. |
| title |
Multi-solid varieties and Mh-transducers |
| title_short |
Multi-solid varieties and Mh-transducers |
| title_full |
Multi-solid varieties and Mh-transducers |
| title_fullStr |
Multi-solid varieties and Mh-transducers |
| title_full_unstemmed |
Multi-solid varieties and Mh-transducers |
| title_sort |
multi-solid varieties and mh-transducers |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152366 |
| citation_txt |
Multi-solid varieties and Mh-transducers / S. Shtrakov
// Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 113–131. — Бібліогр.: 10 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT shtrakovs multisolidvarietiesandmhtransducers |
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2023-05-20T17:38:10Z |
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2023-05-20T17:38:10Z |
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1796153742272233472 |