Andrei Păun

Small universal spiking neural P systems.

In search for small universal computing devices of various types, we consider here the case of spiking neural P systems (SN P systems), in two variants: as devices that compute functions and as devices that generate sets of numbers. We start with the first case and we produce a universal spiking neural P system with 84 neurons. If a slight generalization of the used rules is adopted, namely, we allow rules for producing simultaneously several spikes, then a considerable reduction, to 49 neurons, is obtained. For SN P systems used as generators of sets of numbers, we find a universal system with restricted rules having 76 neurons and one with extended rules having 50 neurons.

Spiking neural P systems with extended rules: universality and languages

We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.

Simulating FAS-induced apoptosis by using P systems

In contrast to differential equations, P systems are an unconventional model of computation which takes into consideration the discrete character of the quantity of components and the inherent randomness that exists in biological phenomena. The key feature of P systems is their compartmentalised structure which represents the heterogeneity of the structural organisation of the cells, and where one can take into account the role played by membranes in the functioning of the system, for example signalling at the cell surface, selective uptake of substances from the media, diffusion across different compartments, etc. We show here that P systems can be a reliable tool for Systems Biology and could even outperform in some cases the current simulation techniques based on differential equations. We will also use a strategy based on the well known Gillespie algorithm but running on more than one compartment called Multi-compartmental Gillespie Algorithm.

COMPUTING BY COMMUNICATION IN NETWORKS OF MEMBRANES

In this paper we consider networks of membranes which compute by communication only, using symport/antiport rules. Such rules are used both for communication with the environment and for direct communication among membranes. It turns out that, rather surprisingly, networks with a small number of membranes are computationally universal. This is proved both for the case of three membranes where each membrane communicates with each other membrane, and for the case of four membranes consisting of two pairs such that only the membranes within each pair communicate directly. A single pair of communicating membranes can compute the Parikh images of matrix languages. Several open problems are also formulated.

Computing with Spiking Neural P Systems: Traces and Small Universal Systems

Recently, the idea of spiking neurons and thus of computing by spiking was incorporated into membrane computing, and so-called spiking neural P systems (abbreviated SN P systems) were introduced. Very shortly, in these systems neurons linked by synapses communicate by exchanging identical signals (spikes), with the information encoded in the distance between consecutive spikes. Several ways of using such devices for computing were considered in a series of papers, with universality results obtained in the case of computing numbers, both in the generating and the accepting mode; generating, accepting, or processing strings or infinite sequences was also proved to be of interest.

On spiking neural p systems and partially blind counter machines

A k-output spiking neural P system (SNP) with output neurons, O1, ..., Ok, generates a tuple (n1, ..., nk) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each Oi generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is ni. After the output neurons generate their pairs of spikes, the system eventually halts. We give characterizations of sets definable by partially blind multicounter machines in terms of k-output SNPs operating in a sequential mode. Slight variations of the models make them universal.

On Membrane Computing Based on Splicing

This paper is a direct continuation of [11]. Characterizations of recursively enumerable languages are given, by means of splicing P systems, having splicing rules of small size (that is, involving short context strings). Also it is shown that with only two membranes we can generate all the recursively enumerable languages; this improves a result from [11], where three membranes are used.

P systems with active membranes and without polarizations

P systems with active membranes but without using electrical charges (polarizations) are shown to be complete for generating recursively enumerable string languages when working on string objects and using only rules with membrane transitions as well as rules with membrane dissolving and elementary membrane division, but also when using various other kinds of rules, even including a new type of rules allowing for membrane generation. In particular, allowing for changing membrane labels turns out to be a very powerful control feature.

P systems with proteins on membranes and membrane division

In this paper we present a method for solving the NP-complete SAT problem using the type of P systems that is defined in [9]. The SAT problem is solved in O(nm) time, where n is the number of boolean variables and m is the number of clauses for a instance written in conjunctive normal form. Thus we can say that the solution for each given instance is obtained in linear time. We succeeded in solving SAT by a uniform construction of a deterministic P system which uses rules involving objects in regions, proteins on membranes, and membrane division. We also investigate the computational power of the systems with proteins on membranes and show that the universality can be reached even in the case of systems that do not even use the membrane division and have only one membrane.

Universality of Minimal Symport/Antiport: Five Membranes Suffice

P systems with symport/antiport rules of a minimal size (only one object passes in any direction in a communication step) have been recently proved to be computationally universal. The result originally reported in [2] has been subsequently improved in [6] by showing that six membranes suffice. In [6] it has been also conjectured that at least one membrane can be saved. Here we prove that conjecture: P systems with five membranes and symport/antiport rules of a minimal size are computationally complete. The optimality of this result remains open.