On Straight Words and Minimal Permutators in Finite Transformation Semigroups

  title={On Straight Words and Minimal Permutators in Finite Transformation Semigroups},
  author={A. Egri-Nagy and Chrystopher L. Nehaniv},
Motivated by issues arising in computer science, we investigate the loop-free paths from the identity transformation and corresponding straight words in the Cayley graph of a finite transformation semigroup with a fixed generator set. Of special interest are words that permute a given subset of the state set. Certain such words, called minimal permutators, are shown to comprise a code, and the straight ones comprise a finite code. Thus, words that permute a given subset are uniquely… Expand
Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions
The goals of this work are to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. Expand
WP 1 : Cell Biology , Autopoiesis and Biological Design Patterns D 1 . 4 : Mathematical Models of Gene Expression Computing
Project funded by the European Community under the " Information Society Technology " Programme. Short Description: This report further develops the framework for linking biological behaviour toExpand
On the skeleton of a finite transformation semigroup
Original article can be found at : http://www.info.sciverse.com/ Copyright Eszterhazy Karoly College [Full text of this article is not available in the UHRA]


Cycle Structure in Automata and the Holonomy Decomposition
The investigation shows that the problem of determining holonomy groups can be reduced to the examination of the cycle structure of certain derived automata, bringing closer the possibility of the application of the cascaded decomposition for real-world problems. Expand
Algebraic properties of automata associated to Petri nets and applications to computation in biological systems
A mathematical argument is provided suggesting a reason for the apparent all-pervasiveness of inhibitory connections in living systems and Petri nets with inhibition are shown to be computationally rich, regardless of the particular interpretation method. Expand
Finding Common Motifs with Gaps Using Finite Automata
We present an algorithm that uses finite automata to find the common motifs with gaps occurring in all strings belonging to a finite set S = {S1,S2,...,Sr}. In order to find these common motifs weExpand
Algebraic Hierarchical Decomposition of Finite State Automata: Comparison of Implementations for Krohn-Rhodes Theory
The hierarchical algebraic decomposition of finite state automata (Krohn-Rhodes Theory) has been a mathematical theory without any computational implementations until the present paper, althoughExpand
Classical finite transformation semigroups
CA, MA, NJ, NY, and PA residents, please add sales tax. Canadian residents, please add 5% GST. Please add $5.00 for shipping one book and $1.00 for each additional book. Outside the US and Canada addExpand
Algebraic theory of machines, languages and semigroups
  • M. Arbib
  • Mathematics, Computer Science
  • 1968
Abstract : The book is an integrated exposition of the algebraic, and especially semigroup-theoretic, approach to machines and languages. It is designed to carry the reader from the elementary theoryExpand
Control of G1 arrest after DNA damage.
Levels of p53 protein increased rapidly and transiently after nonlethal doses of gamma irradiation (XRT) in hematopoietic cells with wild-type, but not mutant, p53 genes, and this cell-cycle alteration after XRT was temporally linked to a transient G1 arrest in these cells. Expand
Classical Transformation Semigroups
  • Algebra and Applications, Springer
  • 2009
SgpDec – software package for hierarchical coordinatization of groups and semigroups, implemented in the GAP computer algebra system, Version
  • http://sgpdec.sf.net
  • 2010