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 sub-classes. 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.
Partially supported by MIUR Project “Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali”, by ESF Project “AutoMathA” (2005-2010), by 60 % Projects of University of Catania, Roma “Tor Vergata”, Salerno (2009).
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Anselmo, M., Giammarresi, D., Madonia, M. (2011). Classification of String Languages via Tiling Recognizable Picture Languages. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_7
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DOI: https://doi.org/10.1007/978-3-642-21254-3_7
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