On graph products of automatic monoids
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 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.

Classification : 20M10, 68Q68
Mots-clés : automatic monoid, graph product 
@article{ITA_2001__35_5_403_0,
     author = {Veloso Da Costa, A.},
     title = {On graph products of automatic monoids},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {403--417},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     mrnumber = {1908863},
     zbl = {1019.20028},
     language = {en},
     url = {http://archive.numdam.org/item/ITA_2001__35_5_403_0/}
}
TY  - JOUR
AU  - Veloso Da Costa, A.
TI  - On graph products of automatic monoids
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2001
SP  - 403
EP  - 417
VL  - 35
IS  - 5
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/ITA_2001__35_5_403_0/
LA  - en
ID  - ITA_2001__35_5_403_0
ER  - 
%0 Journal Article
%A Veloso Da Costa, A.
%T On graph products of automatic monoids
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2001
%P 403-417
%V 35
%N 5
%I EDP-Sciences
%U http://archive.numdam.org/item/ITA_2001__35_5_403_0/
%G en
%F ITA_2001__35_5_403_0
Veloso Da Costa, A. On graph products of automatic monoids. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 403-417. http://archive.numdam.org/item/ITA_2001__35_5_403_0/

[1] C.M. Campbell, E.F. Robertson, N. Ruskuc and R.M. Thomas, Automatic Semigroups. Theoret. Comput. Sci. (to appear). | MR | Zbl

[2] A.J. Duncan, E.F. Robertson and N. Ruskuc, Automatic monoids and change of generators. Math. Proc. Cambridge Philos. Soc. 127 (1999) 403-409. | MR | Zbl

[3] E.R. Green, Graph Products of Groups, Ph.D. Thesis. The University of Leeds (1990).

[4] J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979). | MR | Zbl

[5] S. Hermiller and J. Meier, Algorithms and Geometry for Graph Products of Groups. J. Algebra 171 (1995) 230-257. | MR | Zbl

[6] J.M. Howie, An Introduction to Semigroup Theory. Academic Press (1976). | MR | Zbl

[7] P.V. Silva and B. Steinberg, A Geometric Characterization of Automatic Monoids. Universidade do Porto (preprint). | MR | Zbl

[8] P.V. Silva and B. Steinberg, Extensions and Submonoids of Automatic Monoids. Universidade do Porto (preprint). | MR | Zbl

[9] A. Veloso Da Costa, Graph Products of Monoids. Semigroup Forum 63 (2001) 247-277. | MR | Zbl