1,240 research outputs found
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Space complexity equivalence of P systems with active membranes and Turing machines
We prove that arbitrary single-tape Turing machines can be simulated by uniform families of P systems with active membranes with a cubic slowdown and quadratic space overhead. This result is the culmination of a series of previous partial results, finally establishing the equivalence (up to a polynomial) of many space complexity classes defined in terms of P systems and Turing machines. The equivalence we obtained also allows a number of classic computational complexity theorems, such as Savitch's theorem and the space hierarchy theorem, to be directly translated into statements about membrane systems
Subroutines in P Systems and Closure Properties of Their Complexity Classes
The literature on membrane computing describes several variants of P systems
whose complexity classes C are "closed under exponentiation", that is, they satisfy
the inclusion PC C, where PC is the class of problems solved by polynomial-time
Turing machines with oracles for problems in C. This closure automatically implies closure
under many other operations, such as regular operations (union, concatenation,
Kleene star), intersection, complement, and polynomial-time mappings, which are inherited
from P. Such results are typically proved by showing how elements of a family of
P systems can be embedded into P systems simulating Turing machines, which exploit
the elements of as subroutines. Here we focus on the latter construction, abstracting
from the technical details which depend on the speci c variant of P system, in order to
describe a general strategy for proving closure under exponentiation
Complete Problems for a Variant of P Systems with Active Membranes
We identify a family of decision problems that are hard for some complexity
classes defined in terms of P systems with active membranes working in polynomial time.
Furthermore, we prove the completeness of these problems in the case where the systems
are equipped with a form of priority that linearly orders their rules. Finally, we highlight
some possible connections with open problems related to the computational complexity
of P systems with active membranes
Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes
In this paper we consider three restricted variants of P systems with active
membranes: (1) P systems using out communication rules only, (2) P systems using elementary
membrane division and dissolution rules only, and (3) polarizationless P systems
using dissolution and restricted evolution rules only. We show that every problem in P
can be solved with uniform families of any of these variants. This, using known results on
the upper bound of the computational power of variants (1) and (3) yields new characterizations
of the class P. In the case of variant (2) we provide a further characterization
of P by giving a semantic restriction on the computations of P systems of this varian
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 Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420
Characterising the complexity of tissue P systems with fission rules
We analyse the computational efficiency of tissue P systems, a biologically-inspired computing device modelling the communication between cells. In particular, we focus on tissue P systems with fission rules (cell division and/or cell separation), where the number of cells can increase exponentially during the computation. We prove that the complexity class characterised by these devices in polynomial time is exactly P^#P, the class of problems solved by polynomial-time Turing machines with oracles for counting problems
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-
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
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