6,539 research outputs found
Simulating counting oracles with cooperation
We prove that monodirectional shallow chargeless P systems with active
membranes and minimal cooperation working in polynomial time precisely characterise
P#P
k , the complexity class of problems solved in polynomial time by deterministic
Turing machines with a polynomial number of parallel queries to an oracle for a counting
problem
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
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Simulating quantum field theory with a quantum computer
Forthcoming exascale digital computers will further advance our knowledge of
quantum chromodynamics, but formidable challenges will remain. In particular,
Euclidean Monte Carlo methods are not well suited for studying real-time
evolution in hadronic collisions, or the properties of hadronic matter at
nonzero temperature and chemical potential. Digital computers may never be able
to achieve accurate simulations of such phenomena in QCD and other
strongly-coupled field theories; quantum computers will do so eventually,
though I'm not sure when. Progress toward quantum simulation of quantum field
theory will require the collaborative efforts of quantumists and field
theorists, and though the physics payoff may still be far away, it's worthwhile
to get started now. Today's research can hasten the arrival of a new era in
which quantum simulation fuels rapid progress in fundamental physics.Comment: 22 pages, The 36th Annual International Symposium on Lattice Field
Theory - LATTICE201
Monodirectional P Systems
We investigate the in
uence that the
ow of information in membrane systems
has on their computational complexity. In particular, we analyse the behaviour of P systems
with active membranes where communication only happens from a membrane towards
its parent, and never in the opposite direction. We prove that these \monodirectional
P systems" are, when working in polynomial time and under standard complexity-theoretic
assumptions, much less powerful than unrestricted ones: indeed, they characterise classes
of problems de ned by polynomial-time Turing machines with NP oracles, rather than
the whole class PSPACE of problems solvable in polynomial space
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
Ab Initio Modeling of Ecosystems with Artificial Life
Artificial Life provides the opportunity to study the emergence and evolution
of simple ecosystems in real time. We give an overview of the advantages and
limitations of such an approach, as well as its relation to individual-based
modeling techniques. The Digital Life system Avida is introduced and prospects
for experiments with ab initio evolution (evolution "from scratch"),
maintenance, as well as stability of ecosystems are discussed.Comment: 13 pages, 2 figure
Excitable Media Seminar
The simulation data presented here, and the conceptual framework developed for their interpretation are, both, in need of substantial refinement and extension. However, granting that they are initial pointers of some merit, and elementary indicators of general principles, several implications follow: the activity patterns of neurons and their assemblies are\ud
interdependent with the extracellular milieu in which they are embedded, and to whose time varying composition they contribute. The complexity of this interdependence in the temporal dimension forecloses any time and context invariant relation between what the experimenter may consider stimulus input and its representation in neural activity. Hence, ideas of coding by (quasi)-digital neurons are called in question by the mutual interdependence of neurons and their\ud
humoral milieu. Instead, concepts of 'mass action' in the Nervous system gain a new perspective: this time augmented by including the chemical medium surrounding neurons as part of the dynamics of the system as a whole. Accordingly, a meaningful way to describe activity in a neuron assembly would be in terms of a state space in which it can move along an infinite number of trajectories.\u
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