A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time).

We deal with temporal aspects of distributed systems, introducing and studying a new model called timed distributed π-calculus. This model extends distributed π-calculus with timers, transforming the communication channels into temporary resources. Distributed π-calculus describes located interactions between processes with restricted access to resources. We introduce time constraints by considering timeout timers for channels. Combining these timers with types and locations, we provide a formal framework able to describe complex systems with constraints on time and on resource access. Its typing system and operational semantics are presented. It is proved that the passage of time does not interfere with the typing system. The new model is proved to be sound by using a method based on subject reduction.

Abstract. The paper presents a parallel implementation of the membrane systems. We implement the simplest variant of P systems, which however defines the essential features of the membrane systems, and acts as a framework for other variants of P systems with advanced functionalities. The mechanisms used in this implementation could be easily adapted to other versions of P systems with minor changes. The implementation is designed for a cluster of computers; it is written in C++ and it makes use of Message Passing Interface as its communication mechanism.

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Abstract. The paper formally describes an operational semantics of P systems. We present an abstract syntax of P systems, then the notion of configurations, and we define the sets of inference rules corresponding to the three stages of an evolution step: maximal parallel rewriting, parallel communication, and parallel dissolving. Several results assuring the correctness of each set of inference rules are also presented. Finally, we define simulation and bisimulation relations between P systems.

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