P Systems with Minimal Left and Right Insertion and Deletion

Abstract

Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.

One-dimensional Array Grammars and P Systems with Array Insertion and Deletion Rules

“…Every language L ⊆ T * in L * D 1 I 1 can be written in the form T * l ST * r where T l , T r ⊆ T and S is a finite subset of T * . Using the regulating mechanism of P systems, we get a 1 and even obtain computational completeness: Theorem 1 (see [13]…”

“…In [13], left and right insertions and deletions of strings were considered; the corresponding types of grammars using rules inserting strings of length at most k and deleting strings of length at most m are denoted by D m I k .…”

“…In the string case (see [13]), the operations of left and right insertion (I) of strings of length m and left and right deletion (D) of strings of length k were investigated; the corresponding types are abbreviated by D k I m . Every language L ⊆ T * in L * D 1 I 1 can be written in the form T * l ST * r where T l , T r ⊆ T and S is a finite subset of T * .…”

“…There are numerous results establishing the descriptional complexity parameters sufficient to achieve this goal; for an overview of this area we refer to [32,31]. In [13] it was shown that computational completeness can also be obtained with using only insertions and deletions of just one symbol at the ends of a string using the regulating framework of P systems, where the application of rules depends on the membrane region.…”

A Formal Language Model of DNA Polymerase Enzymatic Activity

“…Insertion-deletion systems that are context-free [27], that have one sidedcontext [28] [23], and that are graph controlled [6] were also proposed. P -systems with insertion-deletion rules have been extensively studied in [22] [24] [2] [1] [7] [8]. A type of substitution operation inspired by errors occurring in biologically encoded information was proposed in [16].…”