46 research outputs found
The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules
Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical
systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when
moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in
the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems
is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with
evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper
bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary
between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new
simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution
to the SAT problem
Narrowing Frontiers of Efficiency with Evolutional Communication Rules and Cell Separation
In the framework of Membrane Computing, several efficient solutions to computationally
hard problems have been given. To find new borderlines between families of
P systems that can solve them and the ones that cannot is an important way to tackle the
P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing
from non-efficiency to presumably efficiency. Here, we try to get narrow frontiers, setting
the stage to adapt efficient solutions from a family of P systems to another one. In order
to do that, a solution to the SAT problem is given by means of a family of tissue P systems
with evolutional symport/antiport rules and cell separation with the restriction that both
the left-hand side and the right-hand side of the rules have at most two objects.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600
Time-freeness and Clock-freeness and Related Concepts in P Systems
In the majority of models of P systems, rules are applied at the ticks of a
global clock and their products are introduced into the system for the following step. In
timed P systems, di erent integer durations are statically assigned to rules; time-free P
systems are P systems yielding the same languages independently of these durations. In
clock-free P systems, durations are real and are assigned to individual rule applications; thus, different applications of the same rule may last for a different amount of time. In
this paper, we formalise timed, time-free, and clock-free P system within a framework
for generalised parallel rewriting. We then explore the relationship between these variants
of semantics. We show that clock-free P systems cannot effi ciently solve intractable
problems. Moreover, we consider un-timed systems where we collect the results using
arbitrary timing functions as well as un-clocked P systems where we take the union over
all possible per-instance rule durations. Finally, we also introduce and study mode-free
P systems, whose results do not depend on the choice of a mode within a fixed family of
modes, and compare mode-freeness with clock-freeness
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
On Efficiency of P Systems with Symport/Antiport and Membrane Division
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 to have 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
and membrane division rules where there is not an environment having the property
mentioned above. Specifically, we establish the relationships between the polynomial
complexity class associated with P systems with symport/antiport, membrane division
rules, and with or without environment. As a consequence, we prove that the role of the
environment is irrelevant in order to solve NP–complete problems in an efficient way.Ministerio de Ciencia e Innovación TIN2012-3743
On Distributed Solution to SAT by Membrane Computing
Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called -distributed tissue P systems with evolutional communication and cell division (, for short) is proposed. A uniform solution to the SAT problem by under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform -P protocols are increased with respect to ; while a single communication is shown to be possible for bi-directional uniform -P protocols for any . We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then for solving the SAT problem work no much faster than TPec
Language generating alphabetic flat splicing P systems
An operation on strings, called at splicing was introduced, inspired by a splicing operation on circular strings considered in the study of modelling of the recombinant behaviour of DNA molecules. A simple kind of at splicing, called alphabetic at splicing, allows insertion of a word with a specified start symbol and/or a specified end symbol, between two pre-determined symbols in a given
word. In this work, we consider a P system with only alphabetic at splicing rules as the evolution rules and strings of symbols as objects in its regions. We examine the language generative power of the resulting alphabetic at splicing P systems (AFS P systems, for short). In particular, we show that AFS P systems with two membranes are more powerful in generative power than AFS P systems with a single membrane. We also construct AFS P systems with at most three membranes to generate languages that do not belong to certain other language classes and show an application to generation of chain code pictures
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
Computational Efficiency of P Systems with Symport/Antiport Rules and Membrane Separation
Membrane ssion is a process by which a biological membrane is split into
two new ones in such a way that the contents 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 paper we deal with celllike
P systems with membrane separation rules that use symport/antiport rules (such
systems compute by changing the places of objects with respect to the membranes, and
not by changing the objects themselves) as communication rules. Speci cally we study
a lower bound on the length of communication rules with respect to the computational
e ciency of such kind of membrane systems; that is, their ability to solve computationally
hard problems in polynomial time by trading space for time. The main result of this
paper is the following: communication rules involving at most three objects is enough
to achieve the computational e ciency of P systems with membrane separation. Thus,
a polynomial time solution to SAT problem is provided in this computing framework. It
is known that only problems in P can be solved in polynomial time by using minimal
cooperation in communication rules and membrane separation, so the lower bound of the
e ciency obtained is an optimal bound.Ministerio de Economía y Competitividad TIN2012-3743
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