17,037 research outputs found
Turing machines based on unsharp quantum logic
In this paper, we consider Turing machines based on unsharp quantum logic.
For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce
E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic
Turing machines (EDTMs). We discuss different E-valued recursively enumerable
languages from width-first and depth-first recognition. We find that
width-first recognition is equal to or less than depth-first recognition in
general. The equivalence requires an underlying E value lattice to degenerate
into an MV algebra. We also study variants of ENTMs. ENTMs with a classical
initial state and ENTMs with a classical final state have the same power as
ENTMs with quantum initial and final states. In particular, the latter can be
simulated by ENTMs with classical transitions under a certain condition. Using
these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs
are more powerful than EDTMs. This is a notable difference from the classical
Turing machines.Comment: In Proceedings QPL 2011, arXiv:1210.029
Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems
A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Łukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms
Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity
The computational complexity of internal diffusion-limited aggregation (DLA)
is examined from both a theoretical and a practical point of view. We show that
for two or more dimensions, the problem of predicting the cluster from a given
set of paths is complete for the complexity class CC, the subset of P
characterized by circuits composed of comparator gates. CC-completeness is
believed to imply that, in the worst case, growing a cluster of size n requires
polynomial time in n even on a parallel computer.
A parallel relaxation algorithm is presented that uses the fact that clusters
are nearly spherical to guess the cluster from a given set of paths, and then
corrects defects in the guessed cluster through a non-local annihilation
process. The parallel running time of the relaxation algorithm for
two-dimensional internal DLA is studied by simulating it on a serial computer.
The numerical results are compatible with a running time that is either
polylogarithmic in n or a small power of n. Thus the computational resources
needed to grow large clusters are significantly less on average than the
worst-case analysis would suggest.
For a parallel machine with k processors, we show that random clusters in d
dimensions can be generated in O((n/k + log k) n^{2/d}) steps. This is a
significant speedup over explicit sequential simulation, which takes
O(n^{1+2/d}) time on average.
Finally, we show that in one dimension internal DLA can be predicted in O(log
n) parallel time, and so is in the complexity class NC
Discrete stochastic models for traffic flow
We investigate a probabilistic cellular automaton model which has been
introduced recently. This model describes single-lane traffic flow on a ring
and generalizes the asymmetric exclusion process models. We study the
equilibrium properties and calculate the so-called fundamental diagrams (flow
vs.\ density) for parallel dynamics. This is done numerically by computer
simulations of the model and by means of an improved mean-field approximation
which takes into account short-range correlations. For cars with maximum
velocity 1 the simplest non-trivial approximation gives the exact result. For
higher velocities the analytical results, obtained by iterated application of
the approximation scheme, are in excellent agreement with the numerical
simulations.Comment: Revtex, 30 pages, full postscript version (including figures)
available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory
"pub/incoming/" paper accepted for publication in Phys.Rev.
Ianus: an Adpative FPGA Computer
Dedicated machines designed for specific computational algorithms can
outperform conventional computers by several orders of magnitude. In this note
we describe {\it Ianus}, a new generation FPGA based machine and its basic
features: hardware integration and wide reprogrammability. Our goal is to build
a machine that can fully exploit the performance potential of new generation
FPGA devices. We also plan a software platform which simplifies its
programming, in order to extend its intended range of application to a wide
class of interesting and computationally demanding problems. The decision to
develop a dedicated processor is a complex one, involving careful assessment of
its performance lead, during its expected lifetime, over traditional computers,
taking into account their performance increase, as predicted by Moore's law. We
discuss this point in detail
Criteria for homotopic maps to be so along monotone homotopies
The state spaces of machines admit the structure of time. A homotopy theory
respecting this additional structure can detect machine behavior unseen by
classical homotopy theory. In an attempt to bootstrap classical tools into the
world of abstract spacetime, we identify criteria for classically homotopic,
monotone maps of pospaces to future homotope, or homotope along homotopies
monotone in both coordinates, to a common map. We show that consequently, a
hypercontinuous lattice equipped with its Lawson topology is future
contractible, or contractible along a future homotopy, if its underlying space
has connected CW type.Comment: 7 pages, 5 figures, partially presented at GETCO 2006. title change;
strengthened Cor. 3.3. -> Prop. 3.7, Prop. 3.2 -> Lem. 3.2; corrected def of
category of continuous lattices in sec. 2; added 5 figures, 8 eg's, Def. 3.4,
Lemmas 2.8, 3.5, refs [1],[4],[5]; rewording throughout; conclusion and
abstract rewritte
From Quantity to Quality: Massive Molecular Dynamics Simulation of Nanostructures under Plastic Deformation in Desktop and Service Grid Distributed Computing Infrastructure
The distributed computing infrastructure (DCI) on the basis of BOINC and
EDGeS-bridge technologies for high-performance distributed computing is used
for porting the sequential molecular dynamics (MD) application to its parallel
version for DCI with Desktop Grids (DGs) and Service Grids (SGs). The actual
metrics of the working DG-SG DCI were measured, and the normal distribution of
host performances, and signs of log-normal distributions of other
characteristics (CPUs, RAM, and HDD per host) were found. The practical
feasibility and high efficiency of the MD simulations on the basis of DG-SG DCI
were demonstrated during the experiment with the massive MD simulations for the
large quantity of aluminum nanocrystals (-). Statistical
analysis (Kolmogorov-Smirnov test, moment analysis, and bootstrapping analysis)
of the defect density distribution over the ensemble of nanocrystals had shown
that change of plastic deformation mode is followed by the qualitative change
of defect density distribution type over ensemble of nanocrystals. Some
limitations (fluctuating performance, unpredictable availability of resources,
etc.) of the typical DG-SG DCI were outlined, and some advantages (high
efficiency, high speedup, and low cost) were demonstrated. Deploying on DG DCI
allows to get new scientific from the simulated
of numerous configurations by harnessing sufficient computational power to
undertake MD simulations in a wider range of physical parameters
(configurations) in a much shorter timeframe.Comment: 13 pages, 11 pages (http://journals.agh.edu.pl/csci/article/view/106
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples
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