Christiansen Grammar for Some P Systems

Abstract

The main goal of this work is to formally describe P systems. This is a necessary step to subsequently apply Christiansen grammar evolution (an evolutionary tool developed by the authors) for automatic designing of P systems. Their complex structure suggests us two decisions: to restrict our study to a subset of P systems that ease the representation while keeping a suitable complexity and to select a powerful enough formal tool. Our work is restricted to a kind of P system that can simulate any logical function by means of delay symbols and two mobile catalysts. Like in general P systems, some components of these "logical" P systems depend on other components (for example, the number of axioms and regions and the set of possible indexes for the symbols in their rules depend on the membrane structure). So, a formal representation able to handle context dependent constructions is needed. Our work uses Christiansen grammars to describe P systems.