78 research outputs found
P Systems with Minimal Left and Right Insertion and Deletion
In this article we investigate the operations of insertion and deletion performed
at the ends of a string. We show that using these operations in a P systems
framework (which corresponds to using specific variants of graph control), computational
completeness can even be achieved with the operations of left and right insertion and
deletion of only one symbol
Time After Time: Notes on Delays In Spiking Neural P Systems
Spiking Neural P systems, SNP systems for short, are biologically inspired
computing devices based on how neurons perform computations. SNP systems use
only one type of symbol, the spike, in the computations. Information is encoded
in the time differences of spikes or the multiplicity of spikes produced at
certain times. SNP systems with delays (associated with rules) and those
without delays are two of several Turing complete SNP system variants in
literature. In this work we investigate how restricted forms of SNP systems
with delays can be simulated by SNP systems without delays. We show the
simulations for the following spike routing constructs: sequential, iteration,
join, and split.Comment: 11 pages, 9 figures, 4 lemmas, 1 theorem, preprint of Workshop on
Computation: Theory and Practice 2012 at DLSU, Manila together with UP
Diliman, DLSU, Tokyo Institute of Technology, and Osaka universit
Counting Membrane Systems
A decision problem is one that has a yes/no answer, while
a counting problem asks how many possible solutions exist associated
with each instance. Every decision problem X has associated a counting
problem, denoted by #X, in a natural way by replacing the question
âis there a solution?â with âhow many solutions are there?â. Counting
problems are very attractive from a computational complexity point of
view: if X is an NP-complete problem then the counting version #X is
NP-hard, but the counting version of some problems in class P can also
be NP-hard.
In this paper, a new class of membrane systems is presented in order
to provide a natural framework to solve counting problems. The class is
inspired by a special kind of non-deterministic Turing machines, called
counting Turing machines, introduced by L. Valiant. A polynomial-time
and uniform solution to the counting version of the SAT problem (a
well-known #P-complete problem) is also provided, by using a family
of counting polarizationless P systems with active membranes, without
dissolution rules and division rules for non-elementary membranes but
where only very restrictive cooperation (minimal cooperation and minimal
production) in object evolution rules is allowed
Evaluating space measures in P systems
P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented
Priorities, Promoters and Inhibitors in Deterministic Non-Cooperative P Systems
Membrane systems (with symbol objects) are distributed controlled multiset
processing systems. Non-cooperative P systems with either promoters or inhibitors (of
weight not restricted to one) are known to be computationally complete. Since recently,
it is known that the power of the deterministic subclass of such systems is subregular. We
present new results on the weight of promoters and inhibitors, as well as for characterizing
the systems with priorities only
Simulating Turing Machines with Polarizationless P Systems with Active Membranes
We prove that every single-tape deterministic Turing machine working in
t(n)
t(n)
time, for some function
t:NâN
t:NâN
, can be simulated by a uniform family of polarizationless P systems with active membranes. Moreover, this is done without significant slowdown in the working time. Furthermore, if
logt(n)
logâĄt(n)
is space constructible, then the members of the uniform family can be constructed by a family machine that uses
O(logt(n))
O(logâĄt(n))
space.Ministerio de EconomĂa y Competitividad TIN2012-3743
A Computational Complexity Theory in Membrane Computing
In this paper, a computational complexity theory within the framework
of Membrane Computing is introduced. Polynomial complexity classes associated with
di erent models of cell-like and tissue-like membrane systems are de ned and the most
relevant results obtained so far are presented. Many attractive characterizations of P 6=
NP conjecture within the framework of a bio-inspired and non-conventional computing
model are deduced.Ministerio de EducaciĂłn y Ciencia TIN2006-13425Junta de AndalucĂa P08âTIC-0420
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 EconomĂa y Competitividad TIN2017-89842-
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