662,969 research outputs found
Computational Complexity of Simple P Systems
We introduce a new class of membrane systems called simple P systems, and
study its computational complexity using the classical theory. We start by presenting the
knapsack problem and analyzing its space and time complexities. Then we study the
computational complexity of simple P systems by considering the static allocation of
resources enabling the parallel application of the rules. We show that the problem of
allocating resources for simple P systems is NP-complete by reducing it to the knapsack
problem. Thus we express the computational complexity of this class of P systems in
terms of classical complexity theory
The computational complexity of Kauffman nets and the P versus NP problem
Complexity theory as practiced by physicists and computational complexity
theory as practiced by computer scientists both characterize how difficult it
is to solve complex problems. Here it is shown that the parameters of a
specific model can be adjusted so that the problem of finding its global energy
minimum is extremely sensitive to small changes in the problem statement. This
result has implications not only for studies of the physics of random systems
but may also lead to new strategies for resolving the well-known P versus NP
question in computational complexity theory.Comment: 4 pages, no figure
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
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
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
Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics
In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes.Peer reviewe
On the Power of Dissolution in P Systems with Active Membranes
In this paper we study membrane dissolution rules in the
framework of P systems with active membranes but without using electrical
charges. More precisely, we prove that the polynomial computational
complexity class associated with the class of recognizer P systems
with active membranes, without polarizations and without dissolution
coincides with the standard complexity class P. Furthermore, we demonstrate
that if we consider dissolution rules, then the resulting complexity
class contains the class NP.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
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
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