Membrane computing [and graph transformation]

Introduction to membrane computing, with an eye on graph theory issues

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast solution is based on a novel proposal, which dynamically extends P systems with mobile channels. The second solution is substantially longer, but is solely based on classical rules and static channels. In contrast to the previous solutions, which work for tree-based P systems, our solutions synchronize to any subset of the underlying digraph; and do not require membrane polarizations or conditional rules, but require states, as typically used in hyperdag and neural P systems

Edge- and Node-Disjoint Paths in P Systems

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

The computational power of Watson-Crick grammars: Revisited

A Watson-Crick finite automaton is one of DNA computational models using the Watson-Crick complementarity feature of deoxyribonucleic acid (DNA). We are interested in investigating a grammar counterpart of Watson-Crick automata. In this paper, we present results concerning the generative power of Watson-Crick (regular, linear, context-free) grammars. We show that the family of Watson-Crick context-free languages is included in the family of matrix languages

Inverse Dynamical Problems: An Algebraic Formulation Via MP Grammars

Metabolic P grammars are a particular class of multiset rewriting grammars introduced in the MP systems' theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse dynamical problems, based on MP grammars and Kronecker product, is given, for further motivating the correctness of the LGSS (Log-gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving dynamical inverse problems in the MP framework. At the end of the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that de nes an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way