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Bidirectional string assembling systems

Published online by Cambridge University Press:  20 January 2014

Martin Kutrib  and
Matthias Wendlandt
Martin Kutrib
Affiliation:
Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany.. Martin.Kutrib@informatik.uni-giessen.de, matthias.wendlandt@informatik.uni-giessen.de
Matthias Wendlandt
Affiliation:
Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany.. Martin.Kutrib@informatik.uni-giessen.de, matthias.wendlandt@informatik.uni-giessen.de

Abstract

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We introduce and investigate several variants of a bidirectional string assemblingsystem, which is a computational model that generates strings from copies of assemblyunits. The underlying mechanism is based on two-sided piecewise assembly of adouble-stranded sequence of symbols, where the upper and lower strand have to match. Thegenerative capacities and the relative power of the variants are our main interest. Inparticular, we prove that bidirectional string assembling system generate languages notrepresented as any finite concatenation of one-sided string assembling systems. The latterbuild an infinite, strict and tight concatenation hierarchy. Moreover, it is shown thateven the strongest system in question can only generate NL languages, while there areunary regular languages that cannot be derived. Furthermore, a finite strict hierarchywith respect to the different variants considered is shown and closure properties of thelanguages generated are presented.

Keywords

String assemblingdouble-stranded sequencesconcatenation hierarchystatelessmulti-head finite automataclosure properties

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