String Assembling Systems

Abstract

Abstract. We introduce and investigate string assembling systems which form a computational model that generates strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the first symbol of a unit has to be the same as the last symbol of the strand generated so far, as well as by the distinction of assembly units that may appear at the beginning, during, and at the end of the assembling process. We start to explore the generative capacity of string assembling systems. In particular, we prove that any such system can be simulated by some nondeterministic one-way two-head finite automaton, while the stateless version of the two-head finite automaton marks to some extent a lower bound for the generative capacity. Moreover, we obtain several incomparability and undecidability results as well as (non-)closure properties, and present questions for further investigations.Mathematics Subject Classification. 68Q05, 68Q42.

Bidirectional string assembling systems

“…The paper is organized as follows: The next section contains preliminaries and the definition of string assembling systems as well as some meaningful examples that are a starting point to explore the generative capacity of the systems. In particular, by a known result from [5] and an example we obtain that bidirectional string assembling systems are strictly stronger than unidirectional ones. Section 3 is devoted to the question whether or not bidirectional string assembling systems generate merely the concatenation of two languages generated by one-sided systems.…”

“…In [5] it has been shown that the language {a n b n a m | n, m ≥ 1} is not generated by any 1SAS. Therefore, by Example 2.4 we obtain the following inclusion.…”

“…In [5] it has been shown that the family of languages generated by 1SAS is not closed under concatenation. In order to derive the infinite, strict, and tight concatenation hierarchy of 1SAS we consider the four languages…”

“…String assembling systems [5] are language generating devices, where the raw material processed is double stranded in such a way that corresponding symbols have to be identical. In this way the correctness of the complementation of a strand is naturally given.…”

“…Although the basic mechanisms of both types of systems are closely related, their generative capacities differ essentially. In [5] it is shown that the copy language {$ 1 w$ 2 w$ 3 | w ∈ Σ + } is generated by a one-sided string assembling system, while it is not generated by any sticker system. On the other hand, sticker systems can generate all regular languages, whereas it turns out that there is a regular language not generated even by the strongest bidirectional string assembling system under consideration.…”