On The Semantics of Annihilation Rules in Membrane Computing

It is well known that polarizationless recognizer P systems with active membranes, without dissolution, with division of elementary and non-elementary membranes, with antimatter and matter/antimatter annihilation rules can solve all problems in NP when the annihilation rules have (weak) priority over all the other rules. Until now, it was an open problem whether these systems can still solve all NP problems if the priority of the matter/antimatter annihilation rules is removed. In this paper we provide a negative answer to this question: we prove that the class of problems solvable by this model of P systems without priority of the matter/antimatter annihilation rules is exactly P. To the best of our knowledge, this is the rst paper in the literature of P systems where the semantics of applying the rules constitutes a frontier of tractability.Ministerio de Economía y Competitividad TIN2012-3743

Recognizer P Systems with Antimatter

In this paper, we consider recognizer P systems with antimatter and the in uence of the matter/antimatter annihilation rules having weak priority over all the other rules or not. We rst provide a uniform family of P systems with active membranes which solves the strongly NP-complete problem SAT, the Satis ability Problem, without polarizations and without dissolution, yet with division for elementary membranes and with matter/antimatter annihilation rules having weak priority over all the other rules. Then we show that without this weak priority of the matter/antimatter annihilation rules over all the other rules we only obtain the complexity class PMinisterio de Economía y Competitividad TIN2012-3743

Solving SAT with Antimatter in Membrane Computing

The set of NP-complete problems is split into weakly and strongly NP- complete ones. The di erence consists in the in uence of the encoding scheme of the input. In the case of weakly NP-complete problems, the intractability depends on the encoding scheme, whereas in the case of strongly NP-complete problems the problem is intractable even if all data are encoded in a unary way. The reference for strongly NP-complete problems is the Satis ability Problem (the SAT problem). In this paper, we provide a uniform family of P systems with active membranes which solves SAT { without polarizations, without dissolution, with division for elementary membranes and with matter/antimatter annihilation. To the best of our knowledge, it is the rst solution to a strongly NP-complete problem in this P system model.Ministerio de Economía y Competitividad TIN2012-3743

(Tissue) P Systems with Anti-Membranes

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for membranes as objects and anti-membranes as the corresponding annihilation counterpart in P systems. Natural numbers can be represented by the corresponding number of membranes with a speci c label. Computational completeness in this setting then can be obtained with using only elementary membrane division rules, without using objects. A similar result can be obtained for tissue P systems with cell division rules and cell / anti-cell annihilation rules. In both cases, as derivation modes we may take the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects)

A Characterization of PSPACE with Antimatter and Membrane Creation

The use of negative information provides a new tool for exploring the limits of P systems as computational devices. In this paper we prove that the combination of antimatter and annihilation rules (based on the annihilation of physical particles and antiparticles) and membrane creation (based on autopoiesis) provides a P system model able to solve PSPACE-complete problems. Namely, we provide a uniform family of P system in such P system model which solves the satis ability problem for quanti ed Boolean formulas (QSAT). In the second part of the paper, we prove that all the decision problems which can be solved with this P system model belong to the complexity class PSPACE, so this P system model characterises PSPACE.Ministerio de Economía y Competitividad TIN2012-3743

P Systems: from Anti-Matter to Anti-Rules

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for rule labels as objects and anti-rule labels as the corresponding annihilation counterpart in P systems. In the presence of a corresponding anti-rule object, annihilation of a rule object happens before the rule that the rule object represents, can be applied. Applying a rule consumes the corresponding rule object, but may also produce new rule objects as well as anti-rule objects, too. Computational completeness in this setting then can be obtained in a one-membrane P system with non-cooperative rules and rule / anti-rule annihilation rules when using one of the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (i.e., non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects). When using the sequential derivation mode, at least the computational power of partially blind register machines is obtained

Some Quick Research Topics

Some research topics are suggested, in a preliminary form, in most cases dealing with (somewhat nonstandard) extensions of existing types of P systems

Semantics of deductive databases with spiking neural P systems

The integration of symbolic reasoning systems based on logic and connectionist systems based on thefunctioning of living neurons is a vivid research area in computer science. In the literature, one can findmany efforts where different reasoning systems based on different logics are linked to classic artificialneural networks. In this paper, we study the relation between the semantics of reasoning systems basedon propositional logic and the connectionist model in the framework of membrane computing, namely,spiking neural P systems. We prove that the fixed point semantics of deductive databases without nega- tion can be implemented in the spiking neural P systems model and such a model can also deal withnegation if it is endowed with anti-spikes and annihilation rules

NASA Technology Plan 1998

This NASA Strategic Plan describes an ambitious, exciting vision for the Agency across all its Strategic Enterprises that addresses a series of fundamental questions of science and research. This vision is so challenging that it literally depends on the success of an aggressive, cutting-edge advanced technology development program. The objective of this plan is to describe the NASA-wide technology program in a manner that provides not only the content of ongoing and planned activities, but also the rationale and justification for these activities in the context of NASA's future needs. The scope of this plan is Agencywide, and it includes technology investments to support all major space and aeronautics program areas, but particular emphasis is placed on longer term strategic technology efforts that will have broad impact across the spectrum of NASA activities and perhaps beyond. Our goal is to broaden the understanding of NASA technology programs and to encourage greater participation from outside the Agency. By relating technology goals to anticipated mission needs, we hope to stimulate additional innovative approaches to technology challenges and promote more cooperative programs with partners outside NASA who share common goals. We also believe that this will increase the transfer of NASA-sponsored technology into nonaerospace applications, resulting in an even greater return on the investment in NASA