P Systems with Active Membranes and Separation Rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this paper, a new de¯nition of separation rules in P systems with active membranes is given. Under the new de¯nition, the e±ciency and universality of P systems with active membranes and separation rules instead of division are investigated

From distribution to replication in cooperative systems with active membranes: A frontier of the efficiency

P systems with active membranes use evolution, communication, dissolution and division(or separation) rules. They do not use cooperation neither priorities, but they haveelectrical charges associated with membranes, which can be modified by rule applications.The inspiration comes from the behaviourof living cells, who “compute” with theirproteins in order to obtain energy, create components, send information to other cells,kill themselves (in a process called apoptosis), and so on. In these models, mitosisissimulated by divisionrules (for elementary and non-elementary membranes) and meiosis,that is, membrane fission inspiration, is captured in separationrules. The parent’s objectsare replicated into both child membranes when a division occurs, while in the caseof separation, objects are distributed (according to a prefixed partition). In both cases,active membranes have been proved to be too powerful for solving computationally hardproblems in an efficient way. Due to this, polarizationless P systems withactive membraneshave been widely studied from a complexity point of view. Evolution rules simulate the transformation of components in membranes, but it iswell known that in Biology elements interact with each other in order to obtain newcomponents. In this paper, (restricted) cooperation in object evolution rules is considered,and the efficiency of the corresponding models is studied

Further Remarks on P Systems with Active Membranes, Separation, Merging, and Release Rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and con°uent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, Ts. Ishdorj. A universality result related to membrane separation is also obtained

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

Minimal cooperation in polarizationless P systems with active membranes

P systems with active membranes is a well developed framework in the eld of Membrane Computing. Using evolution, communication, dissolution and division rules, we know that some kinds of problems can be solved by those systems, but taking into account which ingredients are used. All these rules are inspired by the behavior of living cells, who \compute" with their proteins in order to obtain energy, create components, send information to other cells, kill themselves (in a process called apoptosis), and so on. But there are other behaviors not captured in this framework. As mitosis is simulated by division rules (for elementary and non-elementary membranes), meiosis, that is, membrane ssion inspiration is captured in separation rules. It di ers from the rst in the sense of duplication of the objects (that is, in division rules, we duplicate the objects not involved in the rule, meanwhile in separation rules we divide the content of the original membrane into the new membranes created). Evolution rules simulate the transformation of components in membranes, but it is well known that elements interact with another ones in order to obtain new components. Cooperation in evolution rules is considered. More speci cally, minimal cooperation (in the sense that only two objects can interact in order to create one or two objects

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

Limits on Efficient Computation in P Systems with Symport/Antiport Rules

Classical membrane systems with symport/antiport rules observe the con- servation law, in the sense that they compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. In these systems the environment plays an active role because the systems not only send objects to the environment, but also bring objects from the environment. In the initial configuration of a system, there is a special alphabet whose elements appear in an arbitrary large number of copies. The ability of these computing devices with infinite copies of some objects has been widely exploited in the design of efficient solutions to computationally hard problems. This paper deals with computational aspects of P systems with symport/antiport rules and membrane division rules or membrane separation rules. Specifically, we study the limitations of such P systems when the only communication rules allowed have length 1.Ministerio de Ciencia e Innovación TIN2012-3743

P Systems with Active Cells

P systems with active membranes is a widely studied framework within the field of Membrane Computing since the creation of the discipline. The abstraction of the structure and behavior of living cells is reflected in the tree-like hierarchy and the kinds of rules that can be used in these kinds of systems. Resembling the organization and communication between cells within tissues that form organs, tissue-like P systems were defined as their abstractions, using symport/antiport rules, that is, moving and exchanging elements from one cell to another one. All the cells are located in an environment where there exist an arbitrary number of some elements. Lately, symport/antiport rules have been used in the framework of cell-like membrane systems in order to study their computational power. Interesting results have been reached, since they act similarly to their counterparts in the framework of tissue P systems. Here, the use of the former defined rules (that is, evolution, communication, dissolution and division/separation rules) is considered, but not working with a tree-like structure. Some remarks about choosing good semantics are given

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

Membrane Fission: A Computational Complexity Perspective

Membrane fission is a process by which a biological membrane is split into two new ones in the manner that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication rules of length at most two, and we prove the computational efficiency of this kind of models when using communication rules of length at most three. Hence, a sharp borderline between tractability and NP–hardness is provided in terms of the length of communication rules.Ministerio de Economía y Competitividad TIN2012-3743