Mario J. Pérez-Jiménez

Applications of membrane computing

From the contents:Introduction.- Bioapplications.- Computer Science Applications.- Linguistics Applications.- Membrane Software.- Selective Bibliography of Membrane Computing.In this paper, we develop an analysis of the Needham-Schroeder Public-Key Protocol in the framework of membrane computing. This analysis is used to validate the protocol and exhibits, as expected, a well known logical attack. The novelty of our approach is to use multiset rewriting in a nest of membranes. The use of membranes enables to tight the conditions for detecting an attack. The approach has been validated by developing a full implementation for several versions of the analysis.

Spike Trains in Spiking Neural P Systems

We continue here the study of the recently introduced spiking neural P systems, which mimic the way that neurons communicate with each other by means of short electrical impulses, identical in shape (voltage), but emitted at precise moments of time. The sequence of moments when a neuron emits a spike is called the spike train (of this neuron); by designating one neuron as the output neuron of a spiking neural P system II, one obtains a spike train of II. Given a specific way of assigning sets of numbers to spike trains of II, we obtain sets of numbers computed by II. In this way, spiking neural P systems become number computing devices. We consider a number of ways to assign (code) sets of numbers to (by) spike trains, and prove then computational completeness: the computed sets of numbers are exactly Turing computable sets. When the number of spikes present in the system is bounded, a characterization of semilinear sets of numbers is obtained. A number of research problems is also formulated.

AN OPTIMIZATION SPIKING NEURAL P SYSTEM FOR APPROXIMATELY SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS

Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system.

Fuzzy reasoning spiking neural P system for fault diagnosis

Spiking neural P systems (SN P systems) have been well established as a novel class of distributed parallel computing models. Some features that SN P systems possess are attractive to fault diagnosis. However, handling fuzzy diagnosis knowledge and reasoning is required for many fault diagnosis applications. The lack of ability is a major problem of existing SN P systems when applying them to the fault diagnosis domain. Thus, we extend SN P systems by introducing some new ingredients (such as three types of neurons, fuzzy logic and new firing mechanism) and propose the fuzzy reasoning spiking neural P systems (FRSN P systems). The FRSN P systems are particularly suitable to model fuzzy production rules in a fuzzy diagnosis knowledge base and their reasoning process. Moreover, a parallel fuzzy reasoning algorithm based on FRSN P systems is developed according to neurons dynamic firing mechanism. Besides, a practical example of transformer fault diagnosis is used to demonstrate the feasibility and effectiveness of the proposed FRSN P systems in fault diagnosis problem.

Tissue P systems with channel states

We consider tissue-like P systems with states associated with the links (we call them synapses) between cells, controlling the passage of objects across the links. We investigate the computing power of such devices for the case of using--in a sequential manner--antiport rules of small weights. Systems with two cells are proved to be universal when having arbitrarily many states and minimal antiport rules, or one state and antiport rules of weight two. Also the systems with arbitrarily many cells, three states, and minimal antiport rules are universal. In contrast, the systems with one cell and any number of states and rules of any weight only compute Parikh sets of matrix languages (generated by matrix grammars without appearance checking); characterizations of Parikh images of matrix languages are obtained for such one-cell systems with antiport rules of a reduced weight.

Computational complexity of tissue-like P systems

Membrane systems, also called P systems, are biologically inspired theoretical models of distributed and parallel computing. This paper presents a new class of tissue-like P systems with cell separation, a feature which allows the generation of new workspace. We study the efficiency of the class of P systems and draw a conclusion that only tractable problems can be efficiently solved by using cell separation and communication rules with the length of at most 1. We further present an efficient (uniform) solution to SAT by using cell separation and communication rules with length at most 6. We conclude that a borderline between efficiency and non-efficiency exists in terms of the length of communication rules (assuming P NP). We discuss future research topics and open problems.

P systems with minimal parallelism

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).

P systems, a new computational modelling tool for systems biology

In this paper we present P systems as a reliable computational modelling tool for Systems Biology that takes into account the discrete character of the quantity of components of biological systems, the inherently randomness in biological phenomena and the key role played by membranes in the functioning of living cells. We will introduce two different strategies for the evolution of P systems, namely, Multi-compartmental Gillespie’s Algorithm based on the well known Gillespie’s Algorithm but running on more than one compartment; and Deterministic Waiting Times Algorithm, an exact deterministic method. In order to illustrate these two strategies we have modelled two biological systems: the EGFR Signalling Cascade and the Quorum Sensing System in the bacterium Vibrio Fischeri. Our simulations results show that for the former system a deterministic approach is valid whereas for the latter a stochastic approach like Multi-compartmental Gillespie’s Algorithm is necessary.

Spiking neural p systems with weights

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved valuesweights, firing thresholds, potential consumed by each rulecan be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, 1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

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.