We study semigroups generated by the restrictions of automaton extension (see, e.g., [3]) and give a characterization of automaton extensions that generate finite semigroups.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1094, author = {Miros\l aw Osys}, title = {Semigroups defined by automaton extension mapping}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {25}, year = {2005}, pages = {103-118}, zbl = {1106.68067}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1094} }
Mirosław Osys. Semigroups defined by automaton extension mapping. Discussiones Mathematicae - General Algebra and Applications, Tome 25 (2005) pp. 103-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1094/
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