22 citations · 93 across the 23 of their papers we have counts for
31 papers
Defining the Crick-Franklin-Watson genes of any robot (equals a finite state machine) and defining the Shannon genetic code attached to each gene. We also define the Krohn-Rhodes complexity of any regular maximal prefix code
John Rhodes
This paper will discuss the relationships among three pillars of mathematics: important research in codes and automata by Marcel-Paul Schutzenberger and others; random walks on fin…
Decidability of Krohn-Rhodes complexity of finite semigroups and automata
Stuart Margolis, John Rhodes, Anne Schilling
When decomposing a finite semigroup into a wreath product of groups and aperiodic semigroups, complexity measures the minimal number of groups that are needed. Determining an algor…
Holonomy theorem for finite semigroups
John Rhodes, Anne Schilling, Pedro V. Silva
We provide a simple proof of the Holonomy Theorem using a new Lyndon-Chiswell length function on the Karnofsky-Rhodes expansion of a semigroup. Unexpectedly, we have both a left an…
Markov chains through semigroup graph expansions (a survey)
John Rhodes, Anne Schilling
We review the recent approach to Markov chains using the Karnofksy-Rhodes and McCammond expansions in semigroup theory by the authors and illustrate them by two examples.
Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Foundations and Structure
Stuart W. Margolis, John Rhodes
We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elem…
Truncated Boolean Representable Simplicial Complexes
Stuart W. Margolis, John Rhodes, Pedro Silva
We extend, in significant ways, the theory of truncated boolean representable simplicial complexes introduced in 2015. This theory, which includes all matroids, represents the larg…