389,161 research outputs found
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Decision Problems For Turing Machines
We answer two questions posed by Castro and Cucker, giving the exact
complexities of two decision problems about cardinalities of omega-languages of
Turing machines. Firstly, it is -complete to determine whether
the omega-language of a given Turing machine is countably infinite, where
is the class of 2-differences of -sets. Secondly,
it is -complete to determine whether the omega-language of a given
Turing machine is uncountable.Comment: To appear in Information Processing Letter
Finding ECM-friendly curves through a study of Galois properties
In this paper we prove some divisibility properties of the cardinality of
elliptic curves modulo primes. These proofs explain the good behavior of
certain parameters when using Montgomery or Edwards curves in the setting of
the elliptic curve method (ECM) for integer factorization. The ideas of the
proofs help us to find new families of elliptic curves with good division
properties which increase the success probability of ECM
Computers and Liquid State Statistical Mechanics
The advent of electronic computers has revolutionised the application of
statistical mechanics to the liquid state. Computers have permitted, for
example, the calculation of the phase diagram of water and ice and the folding
of proteins. The behaviour of alkanes adsorbed in zeolites, the formation of
liquid crystal phases and the process of nucleation. Computer simulations
provide, on one hand, new insights into the physical processes in action, and
on the other, quantitative results of greater and greater precision. Insights
into physical processes facilitate the reductionist agenda of physics, whilst
large scale simulations bring out emergent features that are inherent (although
far from obvious) in complex systems consisting of many bodies. It is safe to
say that computer simulations are now an indispensable tool for both the
theorist and the experimentalist, and in the future their usefulness will only
increase.
This chapter presents a selective review of some of the incredible advances
in condensed matter physics that could only have been achieved with the use of
computers.Comment: 22 pages, 2 figures. Chapter for a boo
Revisiting the Rice Theorem of Cellular Automata
A cellular automaton is a parallel synchronous computing model, which
consists in a juxtaposition of finite automata whose state evolves according to
that of their neighbors. It induces a dynamical system on the set of
configurations, i.e. the infinite sequences of cell states. The limit set of
the cellular automaton is the set of configurations which can be reached
arbitrarily late in the evolution.
In this paper, we prove that all properties of limit sets of cellular
automata with binary-state cells are undecidable, except surjectivity. This is
a refinement of the classical "Rice Theorem" that Kari proved on cellular
automata with arbitrary state sets.Comment: 12 pages conference STACS'1
Using field theory to construct hybrid particle-continuum simulation schemes with adaptive resolution for soft matter systems
We develop a multiscale hybrid scheme for simulations of soft condensed
matter systems, which allows one to treat the system at the particle level in
selected regions of space, and at the continuum level elsewhere. It is derived
systematically from an underlying particle-based model by field theoretic
methods. Particles in different representation regions can switch
representations on the fly, controlled by a spatially varying tuning function.
As a test case, the hybrid scheme is applied to simulate colloid-polymer
composites with high resolution regions close to the colloids. The hybrid
simulations are significantly faster than reference simulations of a pure
particle-based model, and the results are in good agreement.Comment: 8 pages, 3 figure
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