258 research outputs found
Minimal Parallelism and Number of Membrane Polarizations
It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal
P systems with minimal parallelism
A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one
target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this
issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or
a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more
rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first
prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter
case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results
are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time)
(Tissue) P Systems with Vesicles of Multisets
We consider tissue P systems working on vesicles of multisets with the very
simple operations of insertion, deletion, and substitution of single objects.
With the whole multiset being enclosed in a vesicle, sending it to a target
cell can be indicated in those simple rules working on the multiset. As
derivation modes we consider the sequential mode, where exactly one rule is
applied in a derivation step, and the set maximal mode, where in each
derivation step a non-extendable set of rules is applied. With the set maximal
mode, computational completeness can already be obtained with tissue P systems
having a tree structure, whereas tissue P systems even with an arbitrary
communication structure are not computationally complete when working in the
sequential mode. Adding polarizations (-1, 0, 1 are sufficient) allows for
obtaining computational completeness even for tissue P systems working in the
sequential mode.Comment: In Proceedings AFL 2017, arXiv:1708.0622
(Tissue) P Systems with Vesicles of Multisets
We consider tissue P systems working on vesicles of multisets with the very
simple operations of insertion, deletion, and substitution of single objects.
With the whole multiset being enclosed in a vesicle, sending it to a target
cell can be indicated in those simple rules working on the multiset. As
derivation modes we consider the sequential mode, where exactly one rule is
applied in a derivation step, and the set maximal mode, where in each
derivation step a non-extendable set of rules is applied. With the set maximal
mode, computational completeness can already be obtained with tissue P systems
having a tree structure, whereas tissue P systems even with an arbitrary
communication structure are not computationally complete when working in the
sequential mode. Adding polarizations (-1, 0, 1 are sufficient) allows for
obtaining computational completeness even for tissue P systems working in the
sequential mode.Comment: In Proceedings AFL 2017, arXiv:1708.0622
Polarizationless P Systems with Active Membranes Working in the Minimally Parallel Mode
We investigate the computing power and the efficiency of P systems with
active membranes without polarizations, working in the minimally parallel mode. We
prove that such systems are computationally complete and able to solve NP-complete
problems even when the rules are of a restricted form, e.g., for establishing computational
completeness we only need rules handling single objects and no division of non-elementary
membranes is usedMinisterio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58
Further Open Problems in Membrane Computing
A series of open problems and research topics in membrane com-
puting are pointed out, most of them suggested by recent developments in this
area. Many of these problems have several facets and branchings, and further
facets and branchings can surely be found after addressing them in a more
careful manner
On a Paun’s Conjecture in Membrane Systems
We study a P˘aun’s conjecture concerning the unsolvability of
NP–complete problems by polarizationless P systems with active membranes
in the usual framework, without cooperation, without priorities,
without changing labels, using evolution, communication, dissolution and
division rules, and working in maximal parallel manner. We also analyse
a version of this conjecture where we consider polarizationless P systems
working in the minimally parallel manner.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía TIC–58
Design Patterns for Efficient Solutions to NP-Complete Problems in Membrane Computing
Many variants of P systems have the ability to generate an
exponential number of membranes in linear time. This feature has been
exploited to elaborate (theoretical) efficient solutions to NP-complete, or
even harder, problems. A thorough review of the existent solutions shows
the utilization of common techniques and procedures. The abstraction
of the latter into design patterns can serve to ease and accelerate the
construction of efficient solutions to new hard problems.Ministerio de Economía y Competitividad TIN2017-89842-
Complexity aspects of polarizationless membrane systems
We investigate polarizationless P systems with active membranes working in
maximally parallel manner, which do not make use of evolution or communication rules, in
order to find which features are sufficient to efficiently solve computationally hard problems.
We show that such systems are able to solve the PSPACE-complete problem
QUANTIFIED 3-SAT, provided that non-elementary membrane division is controlled by the
presence of a (possibly non-elementary) membrane.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58
Frontiers of Membrane Computing: Open Problems and Research Topics
This is a list of open problems and research topics collected after the Twelfth
Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August
2011), meant initially to be a working material for Tenth Brainstorming Week on
Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was
circulated in several versions before the brainstorming and then modified according to
the discussions held in Sevilla and according to the progresses made during the meeting.
In the present form, the list gives an image about key research directions currently active
in membrane computing
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