Generalized Results on Monoids as Memory

Özlem Salehi
(Boğaziçi University, Department of Computer Engineering)
Flavio D'Alessandro
(Università di Roma "La Sapienza", Dipartimento di Matematica)
A. C. Cem Say
(Boğaziçi University, Department of Computer Engineering)

We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free language that can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of languages recognized by rational monoid automata over finitely generated completely simple or completely 0-simple permutable monoids is a semi-linear full trio. Furthermore, we investigate valence pushdown automata, and prove that they are only as powerful as (finite) valence automata. We observe that certain results proven for monoid automata can be easily lifted to the case of context-free valence grammars.

In Erzsébet Csuhaj-Varjú, Pál Dömösi and György Vaszil: Proceedings 15th International Conference on Automata and Formal Languages (AFL 2017), Debrecen, Hungary, September 4-6, 2017, Electronic Proceedings in Theoretical Computer Science 252, pp. 234–247.
Published: 21st August 2017.

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