(Ultimately Confluent) Parallel Multiset-Rewriting Systems with Context

The aim of this paper is to study the power of parallel multiset- rewriting systems with permitting context (or P systems with non-cooperative rules with promoters). The main result obtained is that if we use promoters of weight two, then the system is universal. Moreover, the construction satis¯es a special property we de¯ne: it is ulti- mately con°uent. This means that if the system allows at least one halting computation, then its ¯nal con¯guration is reachable from any reachable con- ¯guration