Standardized Proofs of PSPACE-completeness of P Systems with Active Membranes

Two proofs have been shown for P systems with active membranes in previ- ously 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

On Complexity Classes of Spiking Neural P Systems

A sequence of papers have been recently published, pointing out various intractable problems which may be solved in certain fashions within the framework of spiking neural (SN) P systems. On the other hand, there are also results demonstrating limitations of SN P systems. In this paper we define recognizer SN P systems providing a general platform for this type of results. We intend to give a more systematic characterization of computational power of variants of SN P systems, and establish their relation to standard complexity classes

Improving the Efficiency of Tissue P Systems with Cell Separation

Cell fission process consists of the division of a cell into two new cells such that the contents of the initial cell is distributed between the newly created cells. This process is modelled by a new kind of cell separation rules in the framework of Membrane Computing. Specifically, in tissue-like membrane systems, cell separation rules have been considered joint with communication rules of the form symport/antiport. These models are able to create an exponential workspace, expressed in terms of the number of cells, in linear time. On the one hand, an efficient and uniform solution to the SAT problem by using cell separation and communication rules with length at most 8 has been recently given. On the other hand, only tractable problems can be efficiently solved by using cell separation and communication rules with length at most 1. Thus, in the framework of tissue P systems with cell separation, and assuming that P ̸= NP, a first frontier between efficiency and non-efficiency is obtained when passing from communication rules with length 1 to communication rules with length at most 8. In this paper we improve the previous result by showing that the SAT problem can be solved by a family of tissue P systems with cell separation in linear time, by using communication rules with length at most 3. Hence, we provide a new tractability borderline: passing from 1 to 3 amounts to passing from non–efficiency to efficiency, assuming that P ̸= NP.Ministerio de Ciencia e Innovación TIN2009-13192Junta de Andalucía P08 – TIC 0420

Spiking Neural P Systems: Stronger Normal Forms

Spiking neural P systems are computing devices recently introduced as a bridge between spiking neural nets and membrane computing. Thanks to the rapid research in this eld there exists already a series of both theoretical and application studies. In this paper we focus on normal forms of these systems while preserving their computational power. We study combinations of existing normal forms, showing that certain groups of them can be combined without loss of computational power, thus answering partially open problems stated in. We also extend some of the already known normal forms for spiking neural P systems considering determinism and strong acceptance condition. Normal forms can speed-up development and simplify future proofs in this area