Bidirectional string assembling systems

Abstract

We introduce and investigate several variants of a bidirectional string assembling system, which is a computational model that generates strings from copies of assembly units. The underlying mechanism is based on two-sided piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generative capacities and the relative power of the variants are our main interest. In particular, we prove that bidirectional string assembling system generate languages not represented as any finite concatenation of one-sided string assembling systems. The latter build an infinite, strict and tight concatenation hierarchy. Moreover, it is shown that even the strongest system in question can only generate NL languages, while there are unary regular languages that cannot be derived. Furthermore, a finite strict hierarchy with respect to the different variants considered is shown and closure properties of the languages generated are presented.