Regulating Rule Application with Membrane Boundaries in P Systems

摘要

Recently a new framework based on multiset approximation spaces were introduced for modeling the abstract notion of "closeness to membranes" in P systems. In real biotic/chemical interactions, however, objects not only have to be close enough to membranes, so that they are able to pass through them, but they also need to be in an unstable state, in a state where they are ready to engage into any type of interactions at all. In order to develop these ideas, we employ multi-set approximation spaces for the description of stability and instability. We also demonstrate how the applicability and the use of reaction rules can be regulated during computations using the notion of membrane boundaries. An important feature of this type of regulation is the fact that it does not rely on the maximal parallel way of rule application, therefore it can be used to enhance the computational power of systems with asynchronous, sequential, or any other type of derivation modes. As an example, we show how P systems can generate any recursively enumerable set of numbers independently of the applied derivation mode, which is interesting, since without membrane boundaries asynchronous or sequential systems generate the Parikh sets of matrix languages only.