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

Classifying States of a Finite Markov Chain with Membrane Computing

In this paper we present a method to classify the states of a finite Markov chain through membrane computing. A specific P system with external output is designed for each boolean matrix associated with a finite Markov chain. The computation of the system allows us to decide the convergence of the process because it determines in the environment the classification of the states (recurrent, absorbent, and transient) as well as the periods of states. The amount of resources required in the construction is polynomial in the number of states of the Markov chain.Ministerio de Ciencia y Educación TIN2005-09345-C04-01Junta de Andalucía TIC-58

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

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-

Towards the Green-Griffiths-Lang conjecture

The Green-Griffiths-Lang conjecture stipulates that for every projective variety X of general type over C, there exists a proper algebraic subvariety of X containing all non constant entire curves f : C $\rightarrow$ X. Using the formalism of directed varieties, we prove here that this assertion holds true in case X satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle TX . We then give a sufficient criterion for the Kobayashi hyperbolicity of an arbitrary directed variety (X,V). This work is dedicated to the memory of Professor Salah Baouendi.Comment: version 2 has been expanded and improved (15 pages

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

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/

Probabilistic Guarded P Systems, A New Formal Modelling Framework

Multienvironment P systems constitute a general, formal framework for modelling the dynamics of population biology, which consists of two main approaches: stochastic and probabilistic. The framework has been successfully used to model biologic systems at both micro (e.g. bacteria colony) and macro (e.g. real ecosystems) levels, respectively. In this paper, we extend the general framework in order to include a new case study related to P. Oleracea species. The extension is made by a new variant within the probabilistic approach, called Probabilistic Guarded P systems (in short, PGP systems). We provide a formal definition, a simulation algorithm to capture the dynamics, and a survey of the associated software.Ministerio de Economía y Competitividad TIN2012- 37434Junta de Andalucía P08-TIC-0420

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

Membrane Computing as a Modelling Tool: Looking Back and Forward from Sevilla

This paper is a tribute to Prof. Mario de Jesús Pérez- Jiménez. An overview of modelling applications in membrane computing has been compiled, trying to narrate it from a historical perspective and including numerous bibliographical references. Since being exhaustive was obviously out of scope, this quick tour on almost two decades of applications is biased, paying special attention to the contributions in which Prof. Pérez-Jiménez and members of his research group were involved.Ministerio de Economía y Competitividad TIN2017-89842-