Classification of string languages via tiling recognizable picture languages

Authors:
Marcella Anselmo;Dora Giammarresi;Maria Madonia
Affiliations:
Dipartimento di Informatica, Università di Salerno I-84084 Fisciano (SA) Italy;Dipartimento di Matematica. Università di Roma "Tor Vergata", Roma, Italy;Dip. Matematica e Informatica, Università di Catania, Catania, Italy
Venue:
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Year:
2011

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Abstract

We introduce the definition of string language S recognized via picture language P and prove that there is a one-to-one correspondence between a linear bounded automaton (LBA) for S and a tiling system for P. As consequence tiling systems become an alternative description for LBA that possibly exploits some geometric properties of lines and shapes inside the rectangular pictures. We are able to show a classification of sub-classes of context-sensitive languages via REC subclasses. Moreover we state some relations among languages in Chomsky's hierarchy (from regular up to context-sensitive) and the corresponding size of the picture languages that recognize them.