The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via Eilenberg’s correspondence. This connection prompted the study of various natural operators on pseudovarieties and led to several important questions, both algebraic and algorithmic. The most important of these questions is decidability: given a finite semigroup is there an algorithm that tests whether it belongs to the pseudovariety? Since the most relevant operators on pseudovarieties do not preserve decidability, one often seeks to establish stronger properties. A key role is played by relatively free profinite semigroups, which is the counterpart of free algebras in universal algebra. The purpose of this paper is to give a brief survey of the state of the art, highlighting some of the main developments and problems.
Read full abstract- All Solutions
Editage
One platform for all researcher needs
Paperpal
AI-powered academic writing assistant
R Discovery
Your #1 AI companion for literature search
Mind the Graph
AI tool for graphics, illustrations, and artwork
Unlock unlimited use of all AI tools with the Editage Plus membership.
Explore Editage Plus - Support
Overview
8208 Articles
Published in last 50 years
Related Topics
Articles published on Main Motivation
Authors
Select Authors
Journals
Select Journals
Duration
Select Duration
7978 Search results
Sort by Recency