23 citations · 52 across the 29 of their papers we have counts for
17 papers · 1 filter
Representation Independent Decompositions of Computation
Attila Egri-Nagy, Chrystopher L. Nehaniv
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups.…
From Relation to Emulation and Interpretation: Computer Algebra Implementation of the Covering Lemma for Finite Transformation Semigroups
Attila Egri-Nagy, Chrystopher L. Nehaniv
We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism $(X,S)\…
Computational Enumeration of Independent Generating Sets of Finite Symmetric Groups
Attila Egri-Nagy, Volker Gebhardt
We developed computer algebra tools for enumerating conjugacy classes of independent subsets and generating sets of symmetric groups up to , and carried out an initial analysi…
Computing Embeddings and Isomorphisms of Finite Semigroups
James East, Attila Egri-Nagy, Andrew R. Francis +1
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus…
Bacterial phylogeny in the Cayley graph
Chad Clark, Attila Egri-Nagy, Andrew R. Francis +1
Many models of genome rearrangement involve operations (e.g. inversions and translocations) that are self-inverse, and hence generate a group acting on the space of genomes. This g…
On the atoms of algebraic lattices arising in -theory
Attila Egri-Nagy, Marcel Jackson, John Rhodes +1
We determine many of the atoms of the algebraic lattices arising in -theory of finite semigroups.
Computational Holonomy Decomposition of Transformation Semigroups
Attila Egri-Nagy, Chrystopher L. Nehaniv
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely foll…
Finite Diagram Semigroups: Extending the Computational Horizon
James East, Attila Egri-Nagy, Andrew R. Francis +1
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagra…
SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups
Attila Egri-Nagy, James D. Mitchell, Chrystopher L. Nehaniv
We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructi…
Algebraic double cut and join -- A group-theoretic approach to the operator on multichromosomal genomes
Sangeeta Bhatia, Attila Egri-Nagy, Andrew R. Francis
Establishing a distance between genomes is a significant problem in computational genomics, because its solution can be used to establish evolutionary relationships including phylo…
Enumerating Transformation Semigroups
James East, Attila Egri-Nagy, James D. Mitchell
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application…
Group-theoretic models of the inversion process in bacterial genomes
Attila Egri-Nagy, Volker Gebhardt, Mark M. Tanaka +1
The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesti…
Skeleton Key: Subduction Classes in Finite Transformation Semigroups and Green's Relations
Attila Egri-Nagy, Chrystopher L. Nehaniv
We establish key connections between Green's - and -relations on a finite semigroup and the subduction relation defined on the image sets of an action of the same s…
The Attractor-Cycle Notation for Finite Transformations
Attila Egri-Nagy, Chrystopher L. Nehaniv
We describe a new notation for finite transformations. This attractor-cycle notation extends the orbit-cycle notation for permutations and builds upon existing transformation notat…
Cascade Product of Permutation Groups
Attila Egri-Nagy, Chrystopher L. Nehaniv
Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is th…
On Straight Words and Minimal Permutators in Finite Transformation Semigroups
Attila Egri-Nagy, 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 finit…
Subgroup Chains and Lagrange Coordinatizations of Finite Permutation Groups
Attila Egri-Nagy, Chrystopher L. Nehaniv
We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how…