Multi-solid varieties and Mh-transducers
We consider the concepts of colored terms and multi-hypersubstitutions. If \(t\in W_\tau(X)\) is a term of type \(\tau\), then any mapping \(\alpha_t:Pos^\mathcal{F}(t)\to \mathbb{N}\) of the non-variable positions of a term into the set of natural numbers is called a coloration of \(t.\) The se...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-8622018-03-21T12:28:31Z Multi-solid varieties and Mh-transducers Shtrakov, Slavcho Colored term; multi-hypersubstitution; deduction of identities 08B15, 03C05, 08A70 We consider the concepts of colored terms and multi-hypersubstitutions. If \(t\in W_\tau(X)\) is a term of type \(\tau\), then any mapping \(\alpha_t:Pos^\mathcal{F}(t)\to \mathbb{N}\) of the non-variable positions of a term into the set of natural numbers is called a coloration of \(t.\) The set \(W_\tau^c(X)\) of colored terms consists of all pairs \(\langle t,\alpha_t\rangle.\) 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 \(\rho = (\sigma_1,\sigma_2,\ldots)\) is a mapping \(\rho:\mathbb{N}\to M\), called a multi-hypersubstitution over \(M\). An identity \(t\approx s\), satisfied in a variety \(V\) is an \(M\)-multi-hyperidentity if its images \(\rho[t\approx s]\) are also satisfied in \(V\) for all \(\rho\in M\). 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/862 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/862/392 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2018-03-21T12:28:31Z |
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OJS |
| language |
English |
| topic |
Colored term multi-hypersubstitution deduction of identities 08B15 03C05 08A70 |
| spellingShingle |
Colored term multi-hypersubstitution deduction of identities 08B15 03C05 08A70 Shtrakov, Slavcho Multi-solid varieties and Mh-transducers |
| topic_facet |
Colored term multi-hypersubstitution deduction of identities 08B15 03C05 08A70 |
| format |
Article |
| author |
Shtrakov, Slavcho |
| author_facet |
Shtrakov, Slavcho |
| author_sort |
Shtrakov, Slavcho |
| 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 |
| description |
We consider the concepts of colored terms and multi-hypersubstitutions. If \(t\in W_\tau(X)\) is a term of type \(\tau\), then any mapping \(\alpha_t:Pos^\mathcal{F}(t)\to \mathbb{N}\) of the non-variable positions of a term into the set of natural numbers is called a coloration of \(t.\) The set \(W_\tau^c(X)\) of colored terms consists of all pairs \(\langle t,\alpha_t\rangle.\) 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 \(\rho = (\sigma_1,\sigma_2,\ldots)\) is a mapping \(\rho:\mathbb{N}\to M\), called a multi-hypersubstitution over \(M\). An identity \(t\approx s\), satisfied in a variety \(V\) is an \(M\)-multi-hyperidentity if its images \(\rho[t\approx s]\) are also satisfied in \(V\) for all \(\rho\in M\). 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/862 |
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AT shtrakovslavcho multisolidvarietiesandmhtransducers |
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2025-07-17T10:36:40Z |
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2025-07-17T10:36:40Z |
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