Linqiang Pan

Spiking Neural P Systems with Neuron Division and Budding

Spiking neural P systems are a class of distributed and parallel computing models inspired by spiking neurons. In this work, the features of neuron division and neuron budding are introduced into the framework of spiking neural P systems, which are processes inspired by neural stem cell division. With neuron division and neuron budding, a spiking neural P system can generate exponential work space in polynomial time as the case for P systems with active membranes. In this way, spiking neural P systems can efficiently solve computationally hard problems by means of a space-time tradeoff, which is illustrated with an efficient solution to SAT problem.

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).

Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources

In this paper we continue previous studies on the computational efficiency of spiking neural P systems, under the assumption that some pre-computed resources of exponential size are given in advance. Specifically, we give a deterministic solution for each of two well known PSPACE-complete problems: QSAT and Q3SAT. In the case of QSAT, the answer to any instance of the problem is computed in a time which is linear with respect to both the number n of Boolean variables and the number m of clauses that compose the instance. As for Q3SAT, the answer is computed in a time which is at most cubic in the number n of Boolean variables.

On the Universality of Axon P Systems

Axon P systems are computing models with a linear structure in the sense that all nodes (i.e., computing units) are arranged one by one along the axon. Such models have a good biological motivation: an axon in a nervous system is a complex information processor of impulse signals. Because the structure of axon P systems is linear, the computational power of such systems has been proved to be greatly restricted; in particular, axon P systems are not universal as language generators. It remains open whether axon P systems are universal as number generators. In this paper, we prove that axon P systems are universal as both number generators and function computing devices, and investigate the number of nodes needed to construct a universal axon P system. It is proved that four nodes (respectively, nine nodes) are enough for axon P systems to achieve universality as number generators (respectively, function computing devices). These results illustrate that the simple linear structure is enough for axon P systems to achieve a desired computational power.

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.

Solving multidimensional 0--1 knapsack problem by P systems with input and active membranes

Membrane systems are biologically motivated theoretical models of distributed and parallel computing. In this paper, we present a membrane algorithm to solve multidimensional 0-1 knapsack problem in linear time by recognizer P systems with input and with active membranes using 2-division. This algorithm can also be modified to solve general 0-1 integer programming problem.

Spiking Neural P Systems With Rules on Synapses Working in Maximum Spikes Consumption Strategy

Spiking neural P systems (SN P systems, for short) are a class of parallel and distributed computation models inspired from the way the neurons process and communicate information by means of spikes. In this paper, we consider a new variant of SN P systems, where each synapse instead of neuron has a set of spiking rules, and the neurons contain only spikes; when the number of spikes in a given neuron is “recognized” by a rule on a synapse leaving from it, the rule is enabled; at a computation step, at most one enabled spiking rule is applied on a synapse, and k spikes are removed from a neuron if the maximum number of spikes that the applied spiking rules on the synapses starting from this neuron consume is k. The computation power of this variant of SN P systems is investigated. Specifically, we prove that such SN P systems can generate or accept any set of Turing computable natural numbers. This result gives an answer to an open problem formulated in Theor. Comput. Sci., vol. 529, pp. 82-95, 2014.

Normal Forms of Spiking Neural P Systems With Anti-Spikes

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a variant of spiking neural P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider normal forms of ASN P systems. Specifically, we prove that ASN P systems with pure spiking rules of categories (a, a) and (a, a̅) without forgetting rules are universal as number generating devices. In an ASN P system with spiking rules of categories (a, a̅) and (a̅, a) without forgetting rules, the neurons change spikes to anti-spikes or change anti-spikes to spikes; such systems are proved to be universal. We also prove that ASN P systems with inhibitory synapses using pure spiking rules of category (a, a) and forgetting rules are universal. These results answer an open problem and improve a corresponding result from [IJCCC, IV(3), 2009, 273-282].

Trading polarizations for labels in P systems with active membranes

Abstract.This paper addresses the problem of removing the polarization of membranes from P systems with active membranes - and this is achieved by allowing the change of membrane labels by means of communication rules or by membrane dividing rules. As consequences of these results, we obtain the universality of P systems with active membranes which are allowed to change the labels of membranes, but do not use polarizations. Universality results are easily obtained also by direct proofs. By direct constructions, we also prove that SAT can be solved in linear time by systems without polarizations and with label changing possibilities. If non-elementary membranes can be divided, then SAT can be solved in linear time without using polarizations and label changing. Several open problems are also formulated.