Multi-solid varieties and Mh-transducers

• Published in: Algebra and Discrete Mathematics
• Date: 2007
• Main Author: Shtrakov, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152366
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Multi-solid varieties and Mh-transducers / S. Shtrakov // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 113–131. — Бібліогр.: 10 назв. — англ.

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.