Generation of Diophantine Sets by Computing P Systems with External Output

In this paper a variant of P systems with external output designed to compute functions on natural numbers is presented. These P systems are stable under composition and iteration of functions. We prove that every diophantine set can be generated by such P systems; then, the universality of this model can be deduced from the theorem by Matiyasevich, Robinson, Davis and Putnam in which they establish that every recursively enumerable set is a diophantine set

Decision P Systems and the P =NP Conjecture

We introduce decision P systems, which are a class of P systems with symbol-objects and external output. The main result of the paper is the following: if there exists an NP–complete problem that cannot be solved in polynomial time, with respect to the input length, by a deterministic decision P system constructed in polynomial time, then P = NP. From Zandron-Ferreti-Mauri’s theorem it follows that if P = NP, then no NP–complete problem can be solved in polynomial time, with respect to the input length, by a deterministic P system with active membranes but without membrane division, constructed in polynomial time from the input. Together, these results give a characterization of P = NP in terms of deterministic P systems

Handling Markov Chains with Membrane Computing

In this paper we approach the problem of computing the n–th power of the transition matrix of an arbitrary Markov chain through membrane computing. The proposed solution is described in a semi–uniform way in the framework of P systems with external output. The amount of resources required in the construction is polynomial in the number of states of the Markov chain and in the power. The time of execution is linear in the power and is independent of the number of states involved in the Markov chain.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Families of languages encoded by SN P systems

[EN] In this work, we propose the study of SN P systems as classical information encoders. By taking the spike train of an SN P system as a (binary) source of information, we can obtain different languages according to a previously defined encoding alphabet. We provide a characterization of the language families generated by the SN P systems in this way. This characterization depends on the way we define the encoding scheme: bounded or not bounded and, in the first case, with one-to-one or non injective encodings. Finally, we propose a network topology in order to define a cascading encoder.Sempere Luna, JM. (2018). Families of languages encoded by SN P systems. Lecture Notes in Computer Science. 10725:262-269. https://doi.org/10.1007/978-3-319-73359-3_17S26226910725Chen, H., Freund, R., Ionescu, M., Păun, G., Pérez-Jiménez, M.J.: On string languages generated by spiking neural P systems. Fundam. Inf. 75(1–4), 141–162 (2007)Chen, H., Ionescu, M., Păun, A., Păun, G., Popa, B.: On trace languages generated by spiking neural P systems. In: Eighth International Workshop on Descriptional Complexity of Formal Systems (DCFS 2006), Las Cruces, New Mexico, USA, pp. 94–105, 21–23 June 2006Csuhaj-Varjú, E., Vaszil, G.: On counter machines versus dP automata. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Y., Rozenberg, G., Salomaa, A. (eds.) CMC 2013. LNCS, vol. 8340, pp. 138–150. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54239-8_11Ibarra, O.H., Leporati, A., Păun, A., Woodworth, S.: Spiking neural P systems. In: Păun, G., Rozenberg, G., Salomaa, A. (eds.) The Oxford Handbook of Membrane Computing, Oxford University Press (2010)Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundam. Inf. 71(2–3), 279–308 (2006)Manca, V.: On the generative power of iterated transduction. In: Ito, M., Păun, G., Yu, S. (eds.) Words, Semigroups, and Transductions, pp. 315–327. World Scientific (2001)Manca, V., Martín-Vide, C., Păun, G.: New computing paradigms suggested by DNA computing: computing by carving. BioSystems 52, 47–54 (1999)Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-642-56196-2Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Spike trains in spiking neural P systems. Int. J. Found. Comput. Sci. 17(4), 975–1002 (2006)Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59136-

Segmentation in 2D and 3D image using Tissue-Like P System

Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform computations by applying a finite set of rules in a synchronous, maximally parallel way. In this paper, we open a new research line: P systems are used in Computational Topology within the context of the Digital Image. We choose for this a variant of P systems, called tissue-like P systems, to obtain in a general maximally parallel manner the segmentation of 2D and 3D images in a constant number of steps. Finally, we use a software called Tissue Simulator to check these systems with some examples

Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

A Multiscale Modeling Framework Based on P Systems

Cellular systems present a highly complex organization at different scales including the molecular, cellular and colony levels. The complexity at each one of these levels is tightly interrelated. Integrative systems biology aims to obtain a deeper understanding of cellular systems by focusing on the systemic and systematic integration of the different levels of organization in cellular systems. The different approaches in cellular modeling within systems biology have been classified into mathematical and computational frameworks. Specifically, the methodology to develop computational models has been recently called executable biology since it produces executable algorithms whose computations resemble the evolution of cellular systems. In this work we present P systems as a multiscale modeling framework within executable biology. P system models explicitly specify the molecular, cellular and colony levels in cellular systems in a relevant and understandable manner. Molecular species and their structure are represented by objects or strings, compartmentalization is described using membrane structures and finally cellular colonies and tissues are modeled as a collection of interacting individual P systems. The interactions between the components of cellular systems are described using rewriting rules. These rules can in turn be grouped together into modules to characterize specific cellular processes. One of our current research lines focuses on the design of cell systems biology models exhibiting a prefixed behavior through the automatic assembly of these cellular modules. Our approach is equally applicable to synthetic as well as systems biology.Kingdom's Engineering and Physical Sciences Research Council EP/ E017215/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/F01855X/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/D019613/

On P Systems as a Modelling Tool for Biological Systems

We introduce a variant of P systems where rules have associated a real number providing a measure for the “intrinsic reactivity”of the rule and roughly corresponding to the kinetic coefficient which, in bio-chemistry, is usually associated to each molecular reaction. The behaviour of these P systems is then defined according to a strategy which, in each step, randomly selects the next rule to be applied depending upon a certain distribution of probabilities. As an application, we present a P system model of the quorum sensing regulatory networks of the bacterium Vibrio Fischeri. In this respect, a formalisation of the network in terms of P systems is provided and some simulation results concerning the behaviour of a colony of such bacteria are reported. We also briefly describe the implementation techniques adopted by pointing out the generality of our approach which appears to be fairly independent from the particular choice of P system variant and the language used to implement it.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

Simulating accepting networks of evolutionary processors with filtered connections by accepting evolutionary P systems

In this work, we propose a variant of P system based on the rewriting of string-objects by means of evolutionary rules. The membrane structure of such a P system seems to be a very natural tool for simulating the filters in accepting networks of evolutionary processors with filtered connections. We discuss an informal construction supporting this simulation. A detailed proof is to be considered in an extended version of this work