Commutative Languages and their Composition by Consensual Methods

Stefano Crespi Reghizzi
(DEIB, Politecnico di Milano and CNR-IEIIT)
Pierluigi San Pietro
(DEIB, Politecnico di Milano and CNR-IEIIT)

Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on – and further developing, our recent results on the family of consensually regular (CREG) languages. A CREG language is defined by a regular language on the alphabet that includes the terminal alphabet and its marked copy. New conditions, for ensuring that the union or concatenation of CREG languages is closed, are presented and applied to the commutative SLIP languages. The paper contributes to the knowledge of the CREG family, and introduces novel techniques for language composition, based on arithmetic congruences that act as language signatures. Open problems are listed.

In Zoltán Ésik and Zoltán Fülöp: Proceedings 14th International Conference on Automata and Formal Languages (AFL 2014), Szeged, Hungary, May 27-29, 2014, Electronic Proceedings in Theoretical Computer Science 151, pp. 216–230.
Published: 21st May 2014.

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