P systems-based Modelling of Cellular Signalling Pathways

Cellular signalling pathways are fundamental to the control and regulation of cell behaviour. Understanding the biosignalling network functions are crucial for studying di erent diseases and for designing e ective therapeutic approaches to them. In this paper we present P systems as a feasible computational modelling tool for cellular signalling pathways that takes into consideration the inherent randomness occurring in biological phenomena and the discrete character of the components of the system. We illustrate these cellular models simulating the EGFR signalling cascade and the FAS{induced apoptosis using a deterministic strategy for evolution of P systems.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

An Approach to Computational Complexity in Membrane Computing

In this paper we present a theory of computational complexity in the framework of membrane computing. Polynomial complexity classes in recognizer membrane systems and capturing the classical deterministic and non-deterministic modes of computation, are introduced. In this context, a characterization of the relation P = NP is described.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

A bioinspired computing approach to model complex systems

The use of models is intrinsic to any scientific activity. In particular, formal/mathematical models provide a relevant tool for scientific investigation. This paper presents a new Membrane Computing based computational paradigm as a framework for modelling processes and real-life phenomena. P systems, devices in Membrane Computing, are not used as a computing paradigm, but rather as a formalism for describing the behaviour of the system to be modelled. They offer an approach to the development of models for biological systems that meets the requirements of a good modelling framework: relevance, understandability, extensibility and computability.Ministerio de Economía y Competitividad TIN2012-3743

Computational Complexity Theory in Membrane Computing: Seventeen Years After

In this work we revisit the basic concepts, definitions of computational complexity theory in membrane computing. The paper also discusses a novel methodology to tackle the P versus NP problem in the context of the aforementioned theory. The methodology is illustrated with a collection of frontiers of tractability for several classes of P systems.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Computing Partial Recursive Functions by Transition P Systems

In this paper a variant of transition P systems with external output designed to compute partial functions on natural numbers is presented. These P systems are stable under composition, iteration and unbounded minimization (μ–recursion) of functions. We prove that every partial recursive function can be computed by such P systems, from which the computational completeness of this model can be deduced.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

Efficiency of Tissue P Systems with Cell Separation

The most investigated variants of P systems in the last years are cell-like models, especially in terms of efficiency. Recently, different new models of tissue-like (symport/antiport) P systems have received important attention. This paper presents a new class of tissue P systems with cell separation, where cell separation can generate new workspace. Its efficiency is investigated, specifically, (a) only tractable problem can be efficiently solved by using cell separation and communication rules with length at most 1, and (b) an efficient (uniform) solution to SAT problem by using cell separation and communication rules with length at most 6 is presented. Further research topics and open problems are discussed, too.Ministerio de Educación y Ciencia TIN2006-13452Junta de Andalucía P08 – TIC 0420

Towards Bridging Two Cell-Inspired Models: P Systems and R Systems

We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the "threshold" and "no permanence" ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics.Junta de Andalucía P08 – TIC 0420

An infinite hierarchy of languages defined by dP systems

Here, we continue the study of the recently introduced dP automata. They are symport/antiport P systems consisting of a number of components, each one accepting a string, and working together in recognizing the concatenation of these separate strings; the overall string is distributed to the dP automaton components in a balanced way, i.e., in equal parts up to one symbol, like in the communication complexity area. The question whether or not the number of components induces an infinite hierarchy of the recognized languages was formulated as an open problem in the literature.Wesolve here affirmatively this question (by connecting P automata with right linear simple matrix grammars), then we also briefly discuss the relation between the balanced and the non-balanced way of splitting the input string among components; settling this latter problem remains as a research topic. Some other open problems are also formulated.Junta de Andalucía P08-TIC-0420

P and dP Automata: A Survey

This is a quick survey of basic notions and results related to P automata (P systems with symport/antiport rules working in the accepting mode), with some emphasis on the recently introduced dP automata (a distributed version of the standard P automata), ending with some open problems and research topics which we find of interest in this area.Junta de Andalucía P08 – TIC 0420

P automata revisited

We continue here the investigation of P automata, in their non-extended case, a class of devices which characterize non-universal family of languages. First, a recent conjecture is confirmed: any recursively enumerable language is obtained from a language recognized by a P automaton, to which an initial (arbitrarily large) string is added. Then, we discuss possibilities of extending P automata, following suggestions from string finite automata. For instance, automata with a memory (corresponding to push-down automata) are considered and their power is briefly investigated, as well as some closure properties of the family of languages recognized by P automata. In the context, a brief survey of results about P and dP automata (a distributed version of P automata) is provided, and several further research topics are formulated.Junta de Andalucía P08-TIC-0420