Flattening P Systems with Active Membranes

Lecture Notes in Computer Science, 2010

Given a transition P system Π with dissolution having several membranes, we construct a P system Π f having only one membrane and rules involving sets of promoters and inhibitors. The evolution of this "flat" P system Π f simulates the evolution of initial transition P system Π by replacing any dissolution stage of a configuration in Π by specific rules application in a configuration of Π f . The transition P systems without dissolution represent a special case of this procedure.

Journal of Membrane Computing, 2021

2015

We study variants of P systems that are working in the sequential mode. Usually, they are not computationally complete, but there are possible extensions that can increase the computation power. Extensions that implement a notion of zero-checking are often computationally complete. P systems with an ability to create new membranes are a rare exception as they are known to be computationally complete even in the sequential mode without using a dedicated zero-check operation. Using sets instead of multisets was inspired by Reaction systems and we show how to use this relaxation in the context of active membranes. We challenge the original definition of a membrane creation because possible multiplicity of labels of child membranes are in conflict with no multiplicity of objects in Reaction systems. We propose more suitable notions of membrane creation and prove computational completeness by simulating a register machine.

Soft Computing, 2005

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and confluent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, T.-O. Ishdorj. A universality result related to membrane separation is also obtained.

Membrane Computing, 2017

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and restricted evolution rules only. We show that every problem in P can be solved with uniform families of any of these variants. This, using known results on the upper bound of the computational power of variants (1) and (3) yields new characterizations of the class P. In the case of variant (2) we provide a further characterization of P by giving a semantic restriction on the computations of P systems of this variant.

Lecture Notes in Computer Science, 2005

P systems (known also as membrane systems) are biologi- cally motivated theoretical models of distributed and parallel comput- ing. The two most interesting questions in the area are completeness (solving every solvable problem) and efficiency (solving a hard problem in feasible time). In this paper we define a general class of P systems covering some biological operations with membranes. We introduce a new operation, called replicative-distribution, into P systems with active membranes. This operation is well motivated from a biological point of view, and elegant from a mathematical point of view. It is both com- putationally powerful and efficient. More precisely, the P systems with active membranes using replicative-distribution rules can compute ex- actly what Turing machines can compute, and can solve NP-complete problems, particularly SAT, in linear time.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2010

We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least √ 2 m among the 2 m possible truth assignments satisfy it? As a consequence, the inclusion PP ⊆ PMC AM(−d,−n) holds: this provides an improved lower bound on the class of languages decidable by this kind of P systems.

Machines, Computations, and Universality, 2004

We introduce a new variant of membrane systems where the rules are directly assigned to membranes (and not to the regions as this is usually observed in the area of membrane systems) and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. For the application of rules leading from

Journal of Membrane Computing, 2021

Catalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining even computational completeness with only one catalyst. Last year we could show that the derivation mode max objects , where we only take those multisets of rules which affect the maximal number of objects in the underlying configuration one catalyst is sufficient for obtaining computational completeness without any other ingredients. In this paper we follow this way of research and show that one catalyst is also sufficient for obtaining computational completeness when using specific variants of derivation modes based on non-extendable multisets of rules: we only take those non-extendable multisets whose application yields the maximal number of generated objects or else those non-extendable multisets whose application yields the maximal difference in the number of objects between the newly generated configuration and the current configuration. A similar computational completeness result can even be obtained when omitting the condition of non-extendability of the applied multisets when taking the maximal difference of objects or the maximal number of generated objects. Moreover, we reconsider simple P system with energy control-both symbol and rule energy-controlled P systems equipped with these new variants of derivation modes yield computational completeness.

New Generation Computing, 2004

In this paper we propose a new way to represent P systems with active membranes based on Logic Programming techniques. This representation allows us to express the set of rules and the configuration of the P system in each step of the evolution as literals of an appropriate language of first order logic. We provide a Prolog program to simulate the evolution of these P systems and present some auxiliary tools to simulate the evolution of a P system with active membranes using 2-division which solves the SAT problem following the techniques presented in 10) .