Boris I. Plotkin

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This paper is tightly connected with the book [25]. Since this book had not been translated from Russian into English we give here the brief review of the basic definitions and results from [25]. We prove also new results of the same spirit. They are related to dimension subgroups, varieties of representations of groups and varieties of associative(More)
Let Θ be a variety of algebras, (H, Ψ, f) be a model, where H is an algebra from Θ, Ψ is a set of relation symbols ϕ, f is an interpretation of all ϕ in H. Let X 0 be an infinite set of variables, Γ be a collection of all finite subsets in X 0 (collection of sorts), Φ be the multi-sorted algebra of formulas. These data define a knowledge base KB(H, Ψ, f).(More)
The Krohn-Rhodes complexity theory for pure (without lin-earity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear automata. This notion is ultimately related with decompositions of linear automata. The study of these decom-positions(More)