Complexity of Finite Semigroups: History and Decidability
StuarT Margolis, John Rhodes, Anne Schilling
TL;DR
This paper surveys the Krohn-Rhodes complexity of finite semigroups and discusses the recent proof establishing its computability, resolving a long-standing open problem in algebra.
Contribution
It provides a comprehensive overview of the history and key results related to the complexity of finite semigroups, highlighting the proof of its decidability.
Findings
The complexity of finite semigroups is computable.
Resolved a 50-year-old open problem.
Summarized the proof of computability.
Abstract
In recent papers, Margolis, Rhodes and Schilling proved that the complexity of a finite semigroup is computable. This solved a problem that had been open for more than 50 years. The purpose of this paper is to survey the basic results of Krohn-Rhodes complexity of finite semigroups and to outline the proof of its computability.
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Taxonomy
Topicssemigroups and automata theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms