Membrane Systems and Petri Net Synthesis

Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

An apparently innocent problem in Membrane Computing

The search for effcient solutions of computationally hard problems by means of families of membrane systems has lead to a wide and prosperous eld of research. The study of computational complexity theory in Membrane Computing is mainly based on the look for frontiers of effciency between different classes of membrane systems. Every frontier provides a powerful tool for tackling the P versus NP problem in the following way. Given two classes of recognizer membrane systems R1 and R2, being systems from R1 non-effcient (that is, capable of solving only problems from the class P) and systems from R2 presumably e cient (that is, capable of solving NP-complete problems), and R2 the same class that R1 with some ingredients added, passing from R1 to R2 is comparable to passing from the non effciency to the presumed effciency. In order to prove that P = NP, it would be enough to, given a solution of an NP-complete problem by means of a family of recognizer membrane systems from R2, try to remove the added ingredients to R2 from R1. In this paper, we study if it is possible to solve SAT by means of a family of recognizer P systems from AM0(�����d;+n), whose non-effciency was demonstrated already

New applications for an old tool

First, the dependency graph technique, not so far from its current application, was developed trying to nd the shortest computations for membrane systems solving instances of SAT. Certain families of membrane systems have been demonstrated to be non-effcient by means of the reduction of nding an accepting computation (respectively, rejecting computation) to the problem of reaching from a node of the dependency graph to another one. In this paper, a novel application to this technique is explained. Supposing that a problem can be solved by means of a kind of membrane systems leads to a contradiction by means of using the dependency graph as a reasoning method. In this case, it is demonstrated that a single system without dissolution, polarizations and cooperation cannot distinguish a single object from more than one object. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.Ministerio de Industria, Economía y Competitividad TIN2017-89842-

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Counting Membrane Systems

A decision problem is one that has a yes/no answer, while a counting problem asks how many possible solutions exist associated with each instance. Every decision problem X has associated a counting problem, denoted by #X, in a natural way by replacing the question “is there a solution?” with “how many solutions are there?”. Counting problems are very attractive from a computational complexity point of view: if X is an NP-complete problem then the counting version #X is NP-hard, but the counting version of some problems in class P can also be NP-hard. In this paper, a new class of membrane systems is presented in order to provide a natural framework to solve counting problems. The class is inspired by a special kind of non-deterministic Turing machines, called counting Turing machines, introduced by L. Valiant. A polynomial-time and uniform solution to the counting version of the SAT problem (a well-known #P-complete problem) is also provided, by using a family of counting polarizationless P systems with active membranes, without dissolution rules and division rules for non-elementary membranes but where only very restrictive cooperation (minimal cooperation and minimal production) in object evolution rules is allowed

The DBSCAN Clustering Algorithm on P Systems

We show how to implement the DBSCAN clustering algorithm (Density Based Spatial Clustering of Applications with Noise) on membrane systems using evolution rules with promoters and priorities

Membrane Systems with Priority, Dissolution, Promoters and Inhibitors and Time Petri Nets

We continue the investigations on exploring the connection between membrane systems and time Petri nets already commenced in [4] by extending membrane systems with promoters/inhibitors, membrane dissolution and priority for rules compared to the simple symbol-object membrane system. By constructing the simulating Petri net, we retain one of the main characteristics of the Petri net model, namely, the firings of the transitions can take place in any order: we do not impose any additional stipulation on the transition sequences in order to obtain a Petri net model equivalent to the general Turing machine. Instead, we substantially exploit the gain in computational strength obtained by the introduction of the timing feature for Petri nets