Computational efficiency of dissolution rules in membrane systems

Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to efficiently solve computationally hard problems. On the one hand, an exponential number of objects generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time. On the other hand, when an exponential number of membranes is created and used as workspace, the situation is very different. Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper. NP-complete problems can be solved in polynomial time using P systems with active membranes and with polarizations, but when electrical charges are not used, then dissolution rules turn out to be very important. We show that in the framework of P systems with active membranes but without polarizations and in the framework of P systems with membrane creation, dissolution rules play a crucial role from the computational efficiency point of view.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

New applications for an old tool

First, the dependency graph technique, not so far from its current application, was developed trying to nd the shortest computations for membrane systems solving instances of SAT. Certain families of membrane systems have been demonstrated to be non-effcient by means of the reduction of nding an accepting computation (respectively, rejecting computation) to the problem of reaching from a node of the dependency graph to another one. In this paper, a novel application to this technique is explained. Supposing that a problem can be solved by means of a kind of membrane systems leads to a contradiction by means of using the dependency graph as a reasoning method. In this case, it is demonstrated that a single system without dissolution, polarizations and cooperation cannot distinguish a single object from more than one object. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.Ministerio de Industria, Economía y Competitividad TIN2017-89842-

Far-infrared polarimetry from the Stratospheric Observatory for Infrared Astronomy

Multi-wavelength imaging polarimetry at far-infrared wavelengths has proven to be an excellent tool for studying the physical properties of dust, molecular clouds, and magnetic fields in the interstellar medium. Although these wavelengths are only observable from airborne or space-based platforms, no first-generation instrument for the Stratospheric Observatory for Infrared Astronomy (SOFIA) is presently designed with polarimetric capabilities. We study several options for upgrading the High-resolution Airborne Wideband Camera (HAWC) to a sensitive FIR polarimeter. HAWC is a 12 x 32 pixel bolometer camera designed to cover the 53 - 215 micron spectral range in 4 colors, all at diffraction-limited resolution (5 - 21 arcsec). Upgrade options include: (1) an external set of optics which modulates the polarization state of the incoming radiation before entering the cryostat window; (2) internal polarizing optics; and (3) a replacement of the current detector array with two state-of-the-art superconducting bolometer arrays, an upgrade of the HAWC camera as well as polarimeter. We discuss a range of science studies which will be possible with these upgrades including magnetic fields in star-forming regions and galaxies and the wavelength-dependence of polarization.Comment: 12 pages, 5 figure

A Computational Complexity Theory in Membrane Computing

In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with di erent models of cell-like and tissue-like membrane systems are de ned and the most relevant results obtained so far are presented. Many attractive characterizations of P 6= NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Polarizationless P Systems with Active Membranes Working in the Minimally Parallel Mode

We investigate the computing power and the efficiency of P systems with active membranes without polarizations, working in the minimally parallel mode. We prove that such systems are computationally complete and able to solve NP-complete problems even when the rules are of a restricted form, e.g., for establishing computational completeness we only need rules handling single objects and no division of non-elementary membranes is usedMinisterio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58

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

Uniform Solution to QSAT Using Polarizationless Active Membranes

It is known that the satisfiability problem (SAT) can be solved a semi- uniform family of deterministic polarizationless P systems with active membranes with non-elementary membrane division. We present a double improvement of this result by showing that the satisfiability of a quantified boolean formula (QSAT) can be solved by a uniform family of P systems of the same kind.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Minimal Parallelism and Number of Membrane Polarizations

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal

Complexity aspects of polarizationless membrane systems

We investigate polarizationless P systems with active membranes working in maximally parallel manner, which do not make use of evolution or communication rules, in order to find which features are sufficient to efficiently solve computationally hard problems. We show that such systems are able to solve the PSPACE-complete problem QUANTIFIED 3-SAT, provided that non-elementary membrane division is controlled by the presence of a (possibly non-elementary) membrane.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Dependency Graph Technique Revisited

The dependency graph technique was initially thought as a method to find short paths in the computation tree of a membrane system using weak metrics. It could be used to obtain reasonably fast SAT-solvers, capable of competing with the ones available in the literature. Later on, they were used as a method to demonstrate the non-efficiency of some membrane systems, capturing the dynamics of the systems by a static directed graph structure. Recently, the dependency graphs have also been used to establish negative results in Membrane Computing. Specifically, in this work, demonstrating the inability of a kind of membrane system to solve some decision problems efficiently by means of a single system.Ministerio de Economía, Industria y Competitividad TIN2017-89842-