Tameness of Pseudovarieties of Semigroups

Tameness of The Pseudovariety Ls1

A class of finite semigroups V is said to be decidable if the membership problem for V has a solution, that is, if we can construct an algorithm to test whether a given semigroup lies in V. Decidability of pseudovarieties is not preserved by some of the most common pseudovariety operators, such as semidirect product, Mal’cev product and join [1, 17]. In particular Rhodes [17] has exhibited a de...

Semidirect Product with an Order-computable Pseudovariety and Tameness

The semidirect product of pseudovarieties of semigroups with an order-computable pseudovariety is investigated. The essential tool is the natural representation of the corresponding relatively free profinite semigroups and how it transforms implicit signatures. Several results concerning the behavior of the operation with respect to various kinds of tameness properties are obtained as applicati...

Tameness of pseudovariety joins

The concept of tameness of a pseudovariety was introduced by Almeida and Steinberg [1] as a tool for proving decidability of the membership problem for semidirect products of pseudovarieties. Recall that the join V ∨ W of two pseudovarieties V and W is the least pseudovariety containing both V and W. This talk is concerned with the problem of proving tameness of joins. This problem was consider...

Decidability and Tameness in the Theory of Finite Semigroups

Tameness of some locally trivial pseudovarieties

Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.