On the Reachability Problem in P Systems with Mobile Membranes

2001

We first give a general result about P systems with symbolobjects, which says that systems with membrane creation with only one initial membrane can simulate usual systems without using additional membranes (and this implies as a direct consequence a recent result of Mutyam and Krithivasan), then we extend the membrane creation feature to P systems with stringobjects and we prove the computational universality of such systems.

Natural Computing, 2010

We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACEcomplete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = PSPACE.

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.

1999

The ambient calculus and the P-systems are models developed in different areas of computer science. Still, they are based on similar concepts and structures and are inspired from the same natural model of computation . On this basis, we point out how to transfer ideas and results from one framework to the other. We prove that any P-system can be simulated in ambient calculus. We also introduce the notion of mobile P-systems, suitable to model and motivate security features for membrane computing.

Two proofs have been shown for P systems with active membranes in previously published papers, demonstrating that these P systems can solve in polynomial time exactly the class of problems PSPACE. Consequently, these P systems are equivalent (up to a polynomial time reduction) to Second Machine Class models as the alternating Turing machine or the PRAM computer. These proofs were based on a modified definition of uniform families of P systems. Here we demonstrate that the results remain valid also in the case of standard definitions.

International Journal of Computer Mathematics, 2006

We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind. We here show that they generate all recursively enumerable languages, and two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case. Then we prove that 10 + m symbols are enough to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of nonnegative integers, only using rules of rewriting and sending objects out. We show that accepting can be done by deterministic systems.

Lecture Notes in Computer Science, 2009

Membrane computing is a formal framework of distributed parallel multiset processing. Due to massive parallelism and exponential space some intractable computational problems can be solved by P systems with active membranes in a polynomial number of steps. In this paper we generalize this approach from decisional problems to the computational ones, by providing a solution of a #P-complete problem, namely to compute the permanent of a binary matrix. The implication of this result to the PP complexity class is discussed and compared to known results about NP ∪ co − NP.

Journal of Membrane Computing

The first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane requires some constant physical space. This is equivalent to using a unary encoding to represent multiplicities for each object and membrane. A different approach can also be considered, having in mind an implementation of P systems in silico; in this case, the multiplicity of each object in each membrane can be stored using binary numbers, thus reducing the amount of needed space. In this paper, we give a formal definition for this alternative space complexity measure, we define the corresponding complexity classes and we compare such classes both with standard space complexity classes and with complexity classes defined in the framework of P systems considering the original definition of space.

In this paper we investigate the use of general topological spaces as control mechanisms for membrane systems. For simplicity, we illustrate our approach by showing how arbitrary topologies can be used to study the behaviour of membrane systems with rewrite and communication rules.

Electronic Notes in Theoretical Computer Science, 2007

We present a translation of the mobile ambients without communication and replication into P systems with mobile membranes. We introduce a set of developmental rules over membranes, and describe the correspondence between the behaviour of an ambient and the evolution of the its translated membrane system. We give an operational correspondence result between the mobile ambients and P systems. Some other properties relating mobile ambients to P systems are presented.