A polynomial alternative to unbounded environment for tissue P systems with cell division

The standard definition of tissue P systems includes a special alphabet whose elements are assumed to appear in the initial configuration of the system in an arbitrarily large number of copies. These objects reside in a distinguished place of the system, called the environment. Such potentially infinite supply of objects seems an unfair tool when designing efficient solutions to computationally hard problems in the framework of membrane computing, by performing a space–time trade-off. This paper deals with computational aspects of tissue P systems with cell division where there is no environment having the property mentioned above. Specifically, we prove that the polynomial complexity classes associated with tissue P systems with cell division and with or without environment are actually identical. As a consequence, we conclude that it is not necessary to have infinitely many copies of some objects in the initial configuration in order to solve NP–complete problems in an efficient way.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

Inference of the drivers of collective movement in two cell types: Dictyostelium and melanoma

Collective cell movement is a key component of many important biological processes, including wound healing, the immune response and the spread of cancers. To understand and influence these movements, we need to be able to identify and quantify the contribution of their different underlying mechanisms. Here, we define a set of six candidate models—formulated as advection–diffusion–reaction partial differential equations—that incorporate a range of cell movement drivers. We fitted these models to movement assay data from two different cell types: Dictyostelium discoideum and human melanoma. Model comparison using widely applicable information criterion suggested that movement in both of our study systems was driven primarily by a self-generated gradient in the concentration of a depletable chemical in the cells' environment. For melanoma, there was also evidence that overcrowding influenced movement. These applications of model inference to determine the most likely drivers of cell movement indicate that such statistical techniques have potential to support targeted experimental work in increasing our understanding of collective cell movement in a range of systems

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-

The Relevance of the Environment on the Efficiency of Tissue P Systems

The efficiency of computational devices is usually expressed in terms of their capability to solve computationally hard problems in polynomial time. This paper focuses on tissue P systems, whose efficiency has been shown for several scenarios where the number of cells in the system can grow exponentially, e.g. by using cell division rules or cell separation rules. Moreover, in the first case it suffices to consider very short communication rules with length bounded by two, and in the second one it is enough to consider communication rules with length at most three. This kind of systems have an environment with the property that objects initially located in it appear in an arbitrarily large number of copies, which is a somewhat unfair condition from a computational complexity point of view. In this context, we study the role played by the environment and its ability to handle infinitely many objects, in particular we consider tissue P systems whose environment is initially empty.Ministerio de Ciencia e Innovación TIN2012-37434Junta de Andalucía P08-TIC-0420

Solving the 3-COL Problem by Using Tissue P Systems without Environment and Proteins on Cells

The 3-COL problem consists on deciding if the regions of a map can be coloured with only three colors bearing in mind that two adjacent regions must be coloured with di erent colors. It is a NP problem and it has been previously used in complexity studies in membrane computing to check the ability of a model for solving problems of such complexity class. Recently, tissue P systems with proteins on cells have been presented and its ability to solve NP-problems has been proved, but it remained as an open question to know if such model was still able to solve such problems if the environment was removed. In this paper we provide an a rmative answer to this question by showing a uniform family of tissue P systems without environment and with proteins on cells which solves the 3-COL problem in linear time

Membrane fission versus cell division: When membrane proliferation is not enough

Cell division is a process that produces two or more cells from one cell by replicating the original chromosomes so that each daughter cell gets a copy of them. Membrane fission is a process by which a biological membrane is split into two new ones in suchamanner that the contents of the initial membrane get distributedor separated among the new membranes. Inspired by these biological phenomena, new kinds of models we reconsidered in the discipline of Membrane Computing, in the context of P systems with active membranes, and tissue P systems that use symport/antiport rules, respectively. This paper combines the two approaches: cell-like P systems with symport/antiport rules and membrane separation are studied, from a computational complexity perspective.Specifically, the role of the environment in the context of cell-like P systems withmembrane separation is established, and additional borderlines between tractability and NP-hardness are summarized.Ministerio de Economía y Competitividad TIN2012- 3743

P systems with evolutional communication and division rules

A widely studied field in the framework of membrane computing is computational complexity theory. While some types of P systems are only capable of efficiently solving problems from the class P, adding one or more syntactic or semantic ingredients to these membrane systems can give them the ability to efficiently solve presumably intractable problems. These ingredients are called to form a frontier of efficiency, in the sense that passing from the first type of P systems to the second type leads to passing from non-efficiency to the presumed efficiency. In this work, a solution to the SAT problem, a well-known NP-complete problem, is obtained by means of a family of recognizer P systems with evolutional symport/antiport rules of length at most (2,1) and division rules where the environment plays a passive role; that is, P systems from CDECˆ(2,1). This result is comparable to the one obtained in the tissue-like counterpart, and gives a glance of a parallelism and the non-evolutionary membrane systems with symport/antiport rulesMinisterio de Ciencia e Innovación TIN2017-89842-

P systems with symport/antiport rules: When do the surroundings matter?

Cell-like P systems where communication between the regions are carried out by rules of type symport/antiport are considered. These systems compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. The environment plays an active role in the sense that it not only can receive objects from the system, but also send objects into it. There is an alphabet associated with the environment whose elements appear in an arbitrary large number of copies at the initial configuration. This property seems too strong from a complexity view, but it has been widely exploited in the design of efficient solutions to computationally hard problems when some mechanisms (inspired by mitosis and membrane fission) allowing to construct an exponential workspace in linear time, are considered. In this paper, complexity aspects of P systems with symport/antiport rules and membrane division are considered when the set associated with the environment is the emptyset. It is shown that the role of the environment is irrelevant for such kind of P systems, in contrast with the well known results concerning to its relevance when membrane separation is used instead of membrane division.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China 6132010600

Minimal Cooperation in P Systems with Symport/Antiport: A Complexity Approach

Membrane systems with symport/antiport rules compute by just moving objects among membranes, and not by changing the objects themselves. In these systems the environment plays an active role because, not only it receives objects from the system, but it also sends objects into the system. Actually, in this framework it is commonly assumed that an arbitrarily large number of copies of some objects are initially available in the environment. This special feature has been widely exploited for the design of e cient solutions to computationally hard problems in the framework of tissue like P systems able to create an exponential workspace in polynomial time (e.g. via cell division or cell separation rules). This paper deals with cell-like P systems which use symport/antiport rules as communication rules, and the role played by the minimal cooperation is studied from a computational complexity point of view. Speci cally, the limitations on the e ciency of P systems with membrane separation whose symport/antiport rules involve at most two objects are established. In addition, a polynomial time solution to HAM-CYCLE problem, a well known NP-complete problem, by using a family of such kind of P systems with membrane division, is provided. Therefore, in the framework of cell-like P systems with minimal cooperation in communication rules, passing from membrane separation to membrane division amounts to passing from tractability to NP{hardness.Ministerio de Economía y Competitividad TIN2012-3743