Hierarchies of parallel rewriting P systems - a survey

The paper is about some families of rewriting P systems, where the application of evolution rules is extended from the classical sequential rewriting to the parallel one (as, for instance, in Lindenmayer systems). As a result, consistency problems for the communication of strings may arise. Three variants of parallel rewriting P systems (already present in the literature) are considered here, together with the strategies they use to face the communication problem, and some parallelism methods for string rewriting are defined. We give a survey of all known results about each variant and we state some relations among the three variants, thus establishing hierarchies of parallel rewriting P systems. Various open problems related to the subject are also presented.