Polarizationless P Systems with One Active Membrane

The aim of this paper is to study the computational power of P systems with one active membrane without polarizations. For P systems with active membranes, it is known that computational completeness can be obtained with either of the following combinations of features: 1)two polarizations, 2)membrane creation and dissolution, 3)four membranes with three labels, membrane division and dissolution, 4)seven membranes with two labels, membrane division and dissolution. Clearly, with one membrane only object evolution rules and send-out rules are permitted. Two variants are considered: external output and internal output

P Systems with Active Membranes and Two Polarizations

P systems with active membranes using only two electrical charges and only rules of types (a) and (c) assigned to at most two membranes are shown to be computationally complete { thus improving the previous result of this type from the point of view of the number of polarizations as well as with respect to the number of membranes. Allowing a special variant of rules of type (c) to delete symbols by sending them out, even only one membrane is needed. Moreover, we present an algorithm for deterministically deciding SAT in linear time using only two polarizations and global rules of types (a) ; (c), and (e)

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

Complete Problems for a Variant of P Systems with Active Membranes

We identify a family of decision problems that are hard for some complexity classes defined in terms of P systems with active membranes working in polynomial time. Furthermore, we prove the completeness of these problems in the case where the systems are equipped with a form of priority that linearly orders their rules. Finally, we highlight some possible connections with open problems related to the computational complexity of P systems with active membranes

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

An Approach to Computational Complexity in Membrane Computing

In this paper we present a theory of computational complexity in the framework of membrane computing. Polynomial complexity classes in recognizer membrane systems and capturing the classical deterministic and non-deterministic modes of computation, are introduced. In this context, a characterization of the relation P = NP is described.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

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

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

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