Membrane dissolution and division in P

Membrane systems with dividing and dissolving membranes are known to solve PSPACE problems in polynomial time. However, we give a P upperbound on an important restriction of such systems. In particular we examine systems with dissolution, elementary division and where each membrane initially has at most one child membrane. Even though such systems may create exponentially many membranes, each with di erent contents, we show that their power is upperbounded by PJunta de Andalucía TIC-581Ministerio de Educación y Ciencia TIN2006-1342

Limits of the power of Tissue P systems with cell division

Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic opera- tions in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was shown to range between P and NP ? co-NP , thus characterizing some interesting borderlines between tractability and intractability. In this paper we show that com- putational power of these uniform families in polynomial time is limited by the class PSPACE . This class characterizes the power of many clas- sical parallel computing model

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

Design Patterns for Efficient Solutions to NP-Complete Problems in Membrane Computing

Many variants of P systems have the ability to generate an exponential number of membranes in linear time. This feature has been exploited to elaborate (theoretical) efficient solutions to NP-complete, or even harder, problems. A thorough review of the existent solutions shows the utilization of common techniques and procedures. The abstraction of the latter into design patterns can serve to ease and accelerate the construction of efficient solutions to new hard problems.Ministerio de Economía y Competitividad TIN2017-89842-

Counting Membrane Systems

A decision problem is one that has a yes/no answer, while a counting problem asks how many possible solutions exist associated with each instance. Every decision problem X has associated a counting problem, denoted by #X, in a natural way by replacing the question “is there a solution?” with “how many solutions are there?”. Counting problems are very attractive from a computational complexity point of view: if X is an NP-complete problem then the counting version #X is NP-hard, but the counting version of some problems in class P can also be NP-hard. In this paper, a new class of membrane systems is presented in order to provide a natural framework to solve counting problems. The class is inspired by a special kind of non-deterministic Turing machines, called counting Turing machines, introduced by L. Valiant. A polynomial-time and uniform solution to the counting version of the SAT problem (a well-known #P-complete problem) is also provided, by using a family of counting polarizationless P systems with active membranes, without dissolution rules and division rules for non-elementary membranes but where only very restrictive cooperation (minimal cooperation and minimal production) in object evolution rules is allowed

On Eco-Grammar Systems and Artificial Neural Networks

Eco-grammar systems and artificial neural networks have many common features: massive parallelism, independently working elements (agents/neurons), cooperation of the elements and, not least, universal computational power (at least as that of Turing machine). We prove the possibility to simulate each step of a system of one of the types by a fixed number of steps of a system of the other type without loss of parallelism. Moreover, the number of processing elements (neurons, agents) of the model is a function of class O (n), where n is a number of processing elements of the original system

Modeling Plant Development with M Systems

Morphogenetic systems (M systems) have been recently introduced as a computational model aiming at a deeper understanding of morphogenetic phenomena such as growth, self-reproduction, homeostasis and self-healing of evolving systems. M systems hybridize principles common in membrane computing and abstract self-assembly. The model unfolds in a 3D (or generally, dD) space, growing structures that are self-assembled from generalized tiles using shape and location sensitive local rules. The environment provides mutually reacting atomic particles that contribute to growth control. Initial studies of M systems demonstrated their computational universality and efficiency, as well as their robustness to injuries through their self-healing capabilities. Here, we make a systematic comparison of their generativity power with Lindenmayer systems, the best known model of pattern and shape assembly

Simulating Elementary Active Membranes

The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class ^#. This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P systems with this kind of machines: this proves that the two complexity classes coincide, finally solving an open problem by P\u103un on the power of elementary division. The equivalence holds for both uniform and semi-uniform families of P systems, with or without membrane dissolution rules. Furthermore, the inclusion in ^# also holds for the P systems involved in the P conjecture (with elementary division and dissolution but no charges), which improves the previously known upper bound