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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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/862 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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