# On graph products of automatic monoids

@article{Costa2001OnGP, title={On graph products of automatic monoids}, author={A. Veloso da Costa}, journal={RAIRO Theor. Informatics Appl.}, year={2001}, volume={35}, pages={403-417} }

The graph product is an operator mixing direct and free products. It is already known that free
products and direct products of automatic monoids are automatic. The main aim of this paper is to
prove that graph products of automatic monoids of finite geometric type are still automatic.
A similar result for prefix-automatic monoids is established.

## 8 Citations

On Graph Products of Automatic and Biautomatic Monoids

- Mathematics
- 2006

It is shown that the graph product of automatic monoids is always automatic thereby improving on a result by Veloso da Costa [22] who showed this result provided the factors have finite geometric…

Word Equations over Graph Products

- MathematicsInt. J. Algebra Comput.
- 2003

For monoids that satisfy a weak cancellation condition, it is shown that the decidability of the existential theory of word equations is preserved under graph products and the positive theory of a graph product of groups can be reduced to the positive theories of those factors.

GRAPH PRODUCTS OF RIGHT CANCELLATIVE MONOIDS

- MathematicsJournal of the Australian Mathematical Society
- 2009

Abstract Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of…

Finite Derivation Type for Graph Products of Monoids

- Mathematics
- 2016

The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.

Graph products of left abundant monoids

- Mathematics
- 2021

Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then…

R A ] 1 2 Fe b 20 21 GRAPH PRODUCTS OF LEFT ABUNDANT MONOIDS

- Mathematics
- 2021

Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then…

Logical Aspects of Cayley-graphs: the Monoid Case

- MathematicsInt. J. Algebra Comput.
- 2006

It is shown that the decidability of the first-order theory of a structure is preserved by factorized unfoldings, and the class of monoids, for which the Cayley-graph has a decidable first- order theory, is closed under free products.

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