On three variants of rewriting P systems

Parallel Array-rewriting P Systems

A variant of array-rewriting P systems that uses parallel rewriting of arrays in the regions is introduced. The generative power of this model is compared with certain array grammars generating array languages. It is shown that geometric arrays such as hollow rectangles and hollow squares can be generated by parallel array P systems with a priority relation on the rules. The advantage of the pr...

Two Normal Forms for Rewriting P Systems

Rewriting in P Systems: An Algebraic Approach

We relate to the formal definition of a P system with symbol-objects, from Section 3.5 of Chapter 3 of the monograph [2]. We give an equivalent formulation of the symbol-object rewriting rules which occur in one membrane of a P system, reformulation which emphasizes the underlying algebraic structure of commutative monoid with a finite set of generators. We limit ourselves to systems with only ...

Rewriting P Systems with Conditional Communication

A membrane system (P system) is a model of computation inspired by some basic features of the structure and behaviour of living cells. In this paper we consider systems with string-objects processed by rewriting, with the communication controlled by conditions on the contents of the strings. Symbols, substrings (in an arbitrary place, or as a prefix/suffix), or the shape of the whole string are...

Artin groups, rewriting systems and three-manifolds

We construct finite complete rewriting systems for two large classes of Artin groups: those of finite type, and those whose defining graphs are based on trees. The constructions in the two cases are quite different; while the construction for Artin groups of finite type uses normal forms introduced through work on complex hyperplane arrangements, the rewriting systems for Artin groups based on ...