5 papers · 1 filter
Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1
Stuart Margolis, John Rhodes
A smallish monoid M is a monoid that has a unique 0-minimal ideal I(M) that is a 0-simple subsemigroup and such that its regular J -classes are the group of units and the two in I(…
Bases of Permutation Groups and Boolean Representable Simplicial Complexes
Stuart Margolis, John Rhodes
A base of a permutation group (X,G) is a subset B of X such that its pointwise stabilizer is the trivial group. A list (x1,x2, ... ,xk) of elements of X is irredundant if each elem…
Master List of Examples in Complexity Theory of Finite Semigroup Theory
Stuart Margolis, John Rhodes
This document gives a list of finite semigroups that are interesting from the point of view of Krohn-Rhodes complexity theory. The list will be expanded and updates as "time goes b…
Complexity of Finite Semigroups: History and Decidability
StuarT Margolis, John Rhodes, Anne Schilling
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. Th…
Decidability of Krohn-Rhodes complexity for all finite semigroups and automata
Stuart Margolis, John Rhodes, Anne Schilling
The Krohn-Rhodes Theorem proves that a finite semigroup divides a wreath product of groups and aperiodic semigroups. Krohn-Rhodes complexity equals the minimal number of groups tha…