Mihai Ionescu

Spiking Neural P Systems

We bring together two topics recently introduced in membrane computing, the much investigated spiking neural P systems (in short, SN P systems), inspired from the way the neurons communicate through spikes, and the dP systems (distributed P systems, with components which “read” strings from the environment and then cooperate in accepting their concatenation). The goal is to introduce SN dP systems, and to this aim we first introduce SN P systems with the possibility to input, at their request, spikes from the environment; this is done by so-called request rules. A preliminary investigation of the obtained SN dP systems (they can also be called automata) is carried out. As expected, request rules are useful, while the distribution in terms of dP systems can handle languages which cannot be generated by usual SN P systems. We always work with extended SN P systems; the non-extended case, as well as several other natural questions remain open.

Asynchronous spiking neural P systems

We consider here spiking neural P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, a neuron can apply or not apply its rules which are enabled by the number of spikes it contains (further spikes can come, thus changing the rules enabled in the next step). Because the time between two firings of the output neuron is now irrelevant, the result of a computation is the number of spikes sent out by the system, not the distance between certain spikes leaving the system. The additional non-determinism introduced in the functioning of the system by the non-synchronization is proved not to decrease the computing power in the case of using extended rules (several spikes can be produced by a rule). That is, we obtain again the equivalence with Turing machines (interpreted as generators of sets of (vectors of) numbers). However, this problem remains open for the case of standard spiking neural P systems, whose rules can only produce one spike. On the other hand we prove that asynchronous systems, with extended rules, and where each neuron is either bounded or unbounded, are not computationally complete. For these systems, the configuration reachability, membership (in terms of generated vectors), emptiness, infiniteness, and disjointness problems are shown to be decidable. However, containment and equivalence are undecidable.

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.

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.

EXTENDED SPIKING NEURAL P SYSTEMS WITH DECAYING SPIKES AND/OR TOTAL SPIKING

We consider extended variants of spiking neural P systems with decaying spikes (i.e., the spikes have a limited lifetime) and/or total spiking (i.e., the whole contents of a neuron is erased when it spikes). Although we use the extended model of spiking neural P systems, these restrictions of decaying spikes and/or total spiking do not allow for the generation or the acceptance of more than regular sets of natural numbers.

Replicative - distribution rules in p systems with active membranes

P systems (known also as membrane systems) are biologically motivated theoretical models of distributed and parallel computing. The two most interesting questions in the area are completeness (solving every solvable problem) and efficiency (solving a hard problem in feasible time). In this paper we define a general class of P systems covering some biological operations with membranes. We introduce a new operation, called replicative-distribution, into P systems with active membranes. This operation is well motivated from a biological point of view, and elegant from a mathematical point of view. It is both computationally powerful and efficient. More precisely, the P systems with active membranes using replicative-distribution rules can compute exactly what Turing machines can compute, and can solve NP-complete problems, particularly SAT, in linear time.

Boolean circuits and a DNA algorithm in membrane computing

In the present paper we propose a way to simulate Boolean gates and circuits in the framework of P systems with active membranes using inhibiting/de-inhibiting rules. This new approach on the simulation of Boolean gates has the advantage of a self-embedded synchronization, an extra system to solve this problem not being needed. Moreover, the number of membranes and objects we use for the simulation of Boolean gates is only two. NP-complete problems, particularly CIRCUIT-SAT, are also considered here. In addition, we simulate a ‘DNA-like’ way of (experimentally) solving SAT problem using the tools given by polarization, merging, and separation in P systems.

Inhibiting/de-inhibiting rules in p systems

We introduce in the P systems area a mechanism, inspired from neural-cell behavior, which controls computations by inhibiting and de-inhibiting evolution rules. We investigate the computational power of this mechanism in both generative and accepting P systems. In particular, we prove that universality can be obtained by using one catalyst. If we use only non-cooperative rules and one membrane, then we can obtain at least the family of Parikh images of the languages generated by ET0L systems. Several research proposals are also suggested.

THE POWER OF PROGRAMMED GRAMMARS WITH GRAPHS FROM VARIOUS CLASSES

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

P systems with adjoining controlled communication rules

This paper proposes a new model of P systems where the rules are activated by the presence/absence of certain objects in the neighboring regions. We obtain the computational completeness considering only two membranes, external inhibitors, and carriers. Leaving the carriers apart we obtain equivalence with ET0L systems in terms of number sets.