P systems with minimal parallelism

Abstract

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).

Solving complex problems with a bioinspired model

“…This application has had the condition of using the rules in a maximally parallel way although recent findings consider the minimal parallelism of using the rules: "ifat least a rule from a set of rules associated with a membrane or a región can be used, then at least one rule from that membrane or región must be used, without any other restriction" (Ciobanu et al, 2007). This condition also relaxes the requirements of developing new algorithms that implement the rules application phase.…”

Transition and Halting Modes in (Tissue) P Systems

“…There are several possible interpretations of this minimally parallel transition mode which in an informal way can be described as applying multisets such that from every set R j , 1 ≤ j ≤ h, at least one rule -if possible -has to be used (e.g., see [6]). For the basic variant as defined in the following, in each transition step we choose a multiset of rules R from Appl (Π, C, asyn) that cannot be extended to R ∈ Appl (Π, C, asyn) with R R as well as…”

“…In the original model of membrane systems, the objects evolve in a hierarchical membrane structure (see [8], [16]); in tissue P systems (e.g., see [20], [21], and [11]), the cells communicate within an arbitrary graph topology. In the original model of membrane systems, the maximally parallel transition mode was used, yet later on also other new transition modes for P systems and tissue P systems have been introduced and investigated, for example, the sequential and the asynchronous transition mode as well as the minimally parallel transition mode (see [6]). In [12], a formal framework for (tissue) P systems capturing the formal features of these transition modes was developed, based on a general model of membrane systems as a collection of interacting cells containing multisets of objects (compare with the models of networks of cells as discussed in [5] and networks of language processors as considered in [7]).…”

Arithmetic Operations and Factorization using Asynchronous P Systems

“…For considering the asynchronous parallelism, a number of P systems [1,2,3,5,6,7] have been proposed. For example, some sequential P systems [5,7], which assume sequential application of applicable evolution rules, have been proposed.…”

“…In the papers, the computational powers of the sequential P systems are considered, and the P systems has been proved to be universal. For another example, P systems with minimal parallelism are considered in [3] The P system is proved to be universal, and a P system has been proposed for solving SAT in O(n) steps. However, on the P system with minimal parallelism, at least one rule is applied in each membrane if there exists a rule that can be applied for the membrane.…”