A Linear Solution for QSAT with Membrane Creation

The usefulness of P systems with membrane creation for solving NP problems has been previously proved (see [2, 3]), but, up to now, it was an open problem whether such P systems were able to solve PSPACE-complete problems in polynomial time. In this paper we give an answer to this question by presenting a uniform family of P system with membrane creation which solves the QSAT-problem in linear time.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

P systems with evolutional symport and membrane creation rules solving QSAT

P systems are computing devices based on sets of rules that dictate how they work. While some of these rules can change the objects within the system, other rules can even change the own structure, like creation rules. They have been used in cell-like membrane systems with active membranes to efficiently solve NP-complete problems. In this work, we improve a previous result where a uniform family of P systems with evolutional communication rules whose left-hand side (respectively, right-hand side) have most 2 objects (resp., 2 objects) and membrane creation solved SAT efficiently, and we obtain an efficient solution to solve QBF-SAT or QSAT (a PSPACE-complete problem) having at most 1 object (respectively, 1 object) in their left-hand side (resp., right-hand side) and not making use of the environmentMinisterio de Ciencia e Innovación TIN2017-89842-

Characterizing Tractability with Membrane Creation

This paper analyzes the role that membrane dissolution rules play in order to characterize (in the framework of recognizer P systems with membrane creation) the tractability of decision problems that is, the ef cient solvability of problems by deterministic Turing machines. In this context, the use or not of these rules provides an interesting borderline between tractability and (presumable) intractability.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

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

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

Limits on P Systems with Proteins and Without Division

In the field of Membrane Computing, computational complexity theory has been widely studied trying to nd frontiers of efficiency by means of syntactic or semantical ingredients. The objective of this is to nd two kinds of systems, one non-efficient and another one, at least, presumably efficient, that is, that can solve NP-complete prob- lems in polynomial time, and adapt a solution of such a problem in the former. If it is possible, then P = NP. Several borderlines have been defi ned, and new characterizations of different types of membrane systems have been published. In this work, a certain type of P system, where proteins act as a supporting element for a rule to be red, is studied. In particular, while division rules, the abstraction of cellular mitosis is forbidden, only problems from class P can be solved, in contrast to the result obtained allowing them.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600

On a Paun’s Conjecture in Membrane Systems

We study a P˘aun’s conjecture concerning the unsolvability of NP–complete problems by polarizationless P systems with active membranes in the usual framework, without cooperation, without priorities, without changing labels, using evolution, communication, dissolution and division rules, and working in maximal parallel manner. We also analyse a version of this conjecture where we consider polarizationless P systems working in the minimally parallel manner.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía TIC–58

A new perspective on computational complexity theory in Membrane Computing

A single Turing machine can solve decision problems with an in nite number of instances. On the other hand, in the framework of membrane computing, a \solution" to an abstract decision problem consists of a family of membrane systems (where each system of the family is associated with a nite set of instances of the problem to be solved). An interesting question is to analyze the possibility to nd a single membrane system able to deal with the in nitely many instances of a decision problem. In this context, it is fundamental to de ne precisely how the instances of the problem are introduced into the system. In this paper, two different methods are considered: pre-computed (in polynomial time) resources and non-treated resources. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Logarithmic SAT Solution with Membrane Computing

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., which solves SAT in square-root-sublinear time, this paper proposes an orders-of-magnitude-faster solution, running in logarithmic time, and using a small fixed-sized alphabet and ruleset (25 rules). To the best of our knowledge, this is the fastest deterministic solution across all extant P system variants. Like all other cP solutions, it is a complete solution that is not a member of a uniform family (and thus does not require any preprocessing). Consequently, according to another reduction result by Henderson et al., cP systems can also solve k-colouring and several other NP-complete problems in logarithmic time

A Linear Solution of Subset Sum Problem by Using Membrane Creation

Membrane Computing is a branch of Natural Computing which starts from the assumption that the processes taking place in the compartmental structure of a living cell can be interpreted as computations. In this framework, the solution of NP problems is obtained by generating an exponential amount on workspace in polynomial time and using parallelism to check simultaneously all the candidates to solution. We present a solution to the Subset Sum problem for P systems where new membranes are generated from objects.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0