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

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

Minimal cooperation in polarizationless P systems with active membranes

P systems with active membranes is a well developed framework in the eld of Membrane Computing. Using evolution, communication, dissolution and division rules, we know that some kinds of problems can be solved by those systems, but taking into account which ingredients are used. All these rules are inspired by the behavior of living cells, who \compute" with their proteins in order to obtain energy, create components, send information to other cells, kill themselves (in a process called apoptosis), and so on. But there are other behaviors not captured in this framework. As mitosis is simulated by division rules (for elementary and non-elementary membranes), meiosis, that is, membrane ssion inspiration is captured in separation rules. It di ers from the rst in the sense of duplication of the objects (that is, in division rules, we duplicate the objects not involved in the rule, meanwhile in separation rules we divide the content of the original membrane into the new membranes created). Evolution rules simulate the transformation of components in membranes, but it is well known that elements interact with another ones in order to obtain new components. Cooperation in evolution rules is considered. More speci cally, minimal cooperation (in the sense that only two objects can interact in order to create one or two objects

Polarizationless P Systems with Active Membranes: Computational Complexity Aspects

P systems with active membranes, in their classical definition, make use of noncooperative rules only. However, it is well known that in living cells, proteins interact among them yielding new products. Inspired by this biological phenomenon, the previous framework is reformulated in this paper, allowing cooperation in object evolution rules, while removing electrical charges associated with membranes. More precisely, minimal cooperation in object evolution rules is incorporated in polarizationless P systems with active membranes. In this paper, the term “minimal” means that the left-hand side of such rules consists of at most two symbols, and its length is greater than or equal to the corresponding right-hand side. The computational efficiency of this kind of P systems is studied by providing a uniform polynomial-time solution to SAT problem in such manner that only division rules for elementary membranes are used and dissolution rules are forbidden. Bearing in mind that only tractable problems can be efficiently solved by families of polarizationless P systems with active membranes and without dissolution rules, passing from non-cooperation to minimal cooperation in object evolution rules amounts passing from non-efficiency to efficiency in this framework. This frontier of efficiency provides, as any other borderline does, a possible way to address the P versus NP problem.National Natural Science Foundation of China No. 61033003National Natural Science Foundation of China No. 6132010600

Simulating Turing Machines with Polarizationless P Systems with Active Membranes

We prove that every single-tape deterministic Turing machine working in t(n) t(n) time, for some function t:N→N t:N→N , can be simulated by a uniform family of polarizationless P systems with active membranes. Moreover, this is done without significant slowdown in the working time. Furthermore, if logt(n) log⁡t(n) is space constructible, then the members of the uniform family can be constructed by a family machine that uses O(logt(n)) O(log⁡t(n)) space.Ministerio de Economía y Competitividad TIN2012-3743

From distribution to replication in cooperative systems with active membranes: A frontier of the efficiency

P systems with active membranes use evolution, communication, dissolution and division(or separation) rules. They do not use cooperation neither priorities, but they haveelectrical charges associated with membranes, which can be modified by rule applications.The inspiration comes from the behaviourof living cells, who “compute” with theirproteins in order to obtain energy, create components, send information to other cells,kill themselves (in a process called apoptosis), and so on. In these models, mitosisissimulated by divisionrules (for elementary and non-elementary membranes) and meiosis,that is, membrane fission inspiration, is captured in separationrules. The parent’s objectsare replicated into both child membranes when a division occurs, while in the caseof separation, objects are distributed (according to a prefixed partition). In both cases,active membranes have been proved to be too powerful for solving computationally hardproblems in an efficient way. Due to this, polarizationless P systems withactive membraneshave been widely studied from a complexity point of view. Evolution rules simulate the transformation of components in membranes, but it iswell known that in Biology elements interact with each other in order to obtain newcomponents. In this paper, (restricted) cooperation in object evolution rules is considered,and the efficiency of the corresponding models is studied

Trading Polarization for Bi-stable Catalysts in P Systems with Active Membranes

In the last time, several efforts have been made in order to remove polarizations of membranes from P systems with active membranes; the present paper is a contribution in this respect. In order to compensate the loss of power represented by avoiding polarizations, we use bi-stable catalysts. Polarizationless systems with active membranes which use bi-stable catalysts are proven to be computationally complete and able to solve efficiently NP-complete problems. In this paper we present a solution to SAT in linear time. In order to illustrate the presented solution, we also provide a simulation with CLIPS.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution

Recognizer P systems with active membranes have proven to be very powerful computing devices, being able to solve NP-complete decision problems in a polynomial time. However such solutions usually exploit many powerful features, such as electrical charges (polarizations) associated to membranes, evolution rules, communication rules, and strong or weak forms of division rules. In this paper we contribute to the study of the computational power of polarizationless recognizer P systems with active membranes. Precisely, we show that such systems are able to solve in polynomial time the NP-complete decision problem 3-sat by using only dissolution rules and a form of strong division for non–elementary membranes, working in the maximal parallel way

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

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