Finite automata presentable Abelian groups

A Nies, P Semukhin - Annals of Pure and Applied Logic, 2009 - Elsevier
… FA presentable abelian groups … FA presentable groups or monoids is itself FA presentable.
We then use this method to give new examples of FA presentable torsion-free abelian groups

Breaking up finite automata presentable torsion-free abelian groups

G Braun, L Strüngmann - International Journal of Algebra and …, 2011 - World Scientific
… More generally, any torsion-free abelian group that is divisible by infinitely … -presentable
abelian group G is an extension of a finite rank free group by a finite direct sum of Prüfer groups Z…

Describing groups

A Nies - Bulletin of Symbolic Logic, 2007 - cambridge.org
… and the group operation can be recognized by finite automata (… obtain new FA-presentable
abelian groups from given ones. … FA-presentable abelian group, and let A be a abelian group

FA-presentable groups and rings

A Nies, RM Thomas - Journal of Algebra, 2008 - Elsevier
… domain and relations can be checked by finite automata as opposed to Turing machines; we
… an abelian subgroup A of finite index in H. We may assume that A is a free abelian group Zr …

Finite automata presentable abelian groups

A Nies, P Semukhin - International Symposium on Logical Foundations of …, 2007 - Springer
… We give new examples of FA presentable torsion-free abelian groups. Namely, for every …
abelian group which has an FA presentation. We also construct an FA presentation of the group

A decidable expansion of with the independence property

F Point - arXiv preprint arXiv:2309.00392, 2023 - arxiv.org
… We restrict ourselves to a finite automa presentable subclass, … these modules are finitely
generated abelian groups, the class of … We begin by recalling the definition of finite automata. …

Automata presenting structures: A survey of the finite string case

S Rubin - Bulletin of Symbolic Logic, 2008 - cambridge.org
Finite automata are a robust model of computation that seem … classes of structures presentable
by -automata and ( )-tree automata. My … (vi) Every finitely generated Abelian group (G;+) is …

Automatic presentations for semigroups

AJ Cain, G Oliver, N Ruškuc, RM Thomas - Information and Computation, 2009 - Elsevier
… generated commutative semigroups are FA-presentable. We … recognizable by synchronous
finite automata; see Definition … abelian group is the direct sum of finitely many cyclic groups, …

Unary FA-presentable semigroups

AJ Cain, N Ruškuc, RM Thomas - International Journal of Algebra …, 2012 - World Scientific
… (and more generally for possibly non-commutative rings with identity and no zero divisors)
[… Let 3 be a deterministic complete finite automaton recognizing L. Suppose 3 has state set Q, …

Infinite presentability of groups and condensation

R Bieri, Y Cornulier, L Guyot, R Strebel - Journal of the Institute of …, 2014 - cambridge.org
groups, called infinitely independently presentable groups, … to infer that a group is infinitely
independently presentable. In … of an (abelian) minimax group: an abelian group is called …