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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152366 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862665919827804160 |
|---|---|
| author | Shtrakov, S. |
| author_facet | Shtrakov, S. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T15:18:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152366 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:18:42Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Shtrakov, S. 2019-06-10T14:42:55Z 2019-06-10T14:42:55Z 2007 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. https://nasplib.isofts.kiev.ua/handle/123456789/152366 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Multi-solid varieties and Mh-transducers Article published earlier |
| spellingShingle | Multi-solid varieties and Mh-transducers Shtrakov, S. |
| title | 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_short | Multi-solid varieties and Mh-transducers |
| title_sort | multi-solid varieties and mh-transducers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152366 |
| work_keys_str_mv | AT shtrakovs multisolidvarietiesandmhtransducers |