P systems with minimal insertion and deletion

Abstract

In this paper we consider insertion-deletion P systems with priority of deletion over the insertion. We show that such systems with one symbol context-free insertion and deletion rules are able to generate P sRE. If one-symbol one-sided context is added to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important and in its absence the corresponding class of P systems is strictly included in M AT .

P Systems with Minimal Left and Right Insertion and Deletion

“…Using even only the operations of minimal left insertion and minimal right deletion, matrix grammars reach computational completeness with matrices of length at most 3; our conjecture is that this required length cannot be reduced to 2. As our main result, we have shown that sequential P systems using the operations of minimal left and right insertion and deletion are computationally complete, thus solving an open problem from [2]. The simple P system constructed in the proof of Theorem 5 had rather large tree height; it remains an open question to reduce this complexity parameter.…”

“…When one of these parameters is decreased, this result is not true anymore [32]; moreover, even the graph-controlled variant cannot achieve computational completeness [19]. This changes when a graph control with appearance checking is used [1] or in the case of a random context control [16]. In both variants, minimal operations (involving only one symbol) were considered, leading to RE (the family of recursivey enumerable languages) in the case of setcontrolled random context conditions and to P sRE (the family of Parikh sets of RE) in the case of graph control with appearance checking.…”

“…On the other hand, the Dyck language cannot be obtained when insertion is only possible at the ends of the strings, while with normal insertion this can be done easily. In [1,3], left and right insertion and deletion operations (under the name of exo-insertion and -deletion) were considered in the P systems framework (i.e., with a graph control) and it was shown that systems with insertion of strings of length 2 (respectively 1) and deletion of strings of length 1 (respectively 2) lead to computational completeness. In the case of minimal insertion and deletion (i.e., of only one symbol), a priority of deletion over insertion (corresponding to an appearance check) was used to show computational completeness.…”

Random Context and Semi-conditional Insertion-deletion Systems

“…(2) q have been inserted into the string before and after some pairsXX, the rule q.3 will erase an instance ofX; the normalization condition will assure that the erased symbol was located exactly after $ (1) q . The contexts of the rule q.4 guarantee that the proper instance ofX has already been erased (the permitting condition $ (1) qX ) and will block the rule in the cases when $ (1) q is inserted betweenX andX and when $ (2) q is inserted after $ (1) q ; in the latter case q.3 would be blocked. The rule q.5 assures the proper localization of $ (3) q , i.e., before $ (1) q .…”

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].…”