Ultimately Confluent Rewriting Systems. Parallel Multiset-Rewriting with Permitting or Forbidding Contexts

The aim of this paper is to study the power of parallel multiset-rewriting systems with permitting or forbidding context (or P systems with non-cooperative rules with promoters or inhibitors). The main results obtained say that if we use promoters or inhibitors of weight two, then the systems are computational universal. Moreover, both constructions satisfy a special property we define: they are ultimately confluent. This means that if the system allows at least one halting computation, then their final configurations are reachable from any reachable configuration. The other property both constructions satisfy is that a system allowing at least one halting computation will halt with probability 1.