Multiset Patterns and Their Application to Dynamic Causalities in Membrane Systems.

In this paper we investigate dynamic causalities in membrane systems by proposing the concept of “predictor”, originally defined in the context of Ehrenfeucht and Rozemberg’s reaction systems. The goal is to characterize sufficient conditions for the presence of a molecule of interest in the configuration of a P system after a given number of evolution steps (independently from the non-deterministic choices taken). Such conditions can be used to study causal relationships between molecules. To achieve our goal, we introduce the new concept of “multiset pattern” representing a logical formula on multisets. A predictor can be expressed as a pattern characterizing the initial multisets that will surely lead (sufficient condition) to the presence of the molecule of interest after the given number of evolution steps. We define also an operator that computes such a predictor.