Computing Automatic Coset Systems and Subgroup Presentations

Automatic coset systems

Computing coset leaders of binary codes

We present an algorithm for computing the set of all coset leaders of a binary code C ⊂ F n 2. The method is adapted from some of the techniques related to the computation of Gröbner representations associated with codes. The algorithm provides a Gröbner representation of the binary code and the set of coset leaders CL(C). Its efficiency stands of the fact that its complexity is linear on the n...

Automatic presentations for semigroups

This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We giv...

Automatic Presentations for Cancellative Semigroups

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

Automatic presentations of infinite structures

The work at hand studies the possibilities and limitations of the use of finite automata in the description of infinite structures. An automatic presentation of a countable structure consists of a labelling of the elements of the structure by finite words over a finite alphabet in a consistent way so as to allow each of the relations of the structure to be recognised, given the labelling, by a ...