4,308 research outputs found
On the Separability Problem of String Constraints
We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints. We first show that regular separability of straight line string constraints is undecidable. Our second result is the decidability of the separability problem for straight-line string constraints by piece-wise testable languages, though the precise complexity is open. In our third result, we consider the positive fragment of piece-wise testable languages as a separator, and obtain an ExpSpace algorithm for the separability of a useful class of straight-line string constraints, and a Pspace-hardness result
The Novel Approach of Adaptive Twin Probability for Genetic Algorithm
The performance of GA is measured and analyzed in terms of its performance
parameters against variations in its genetic operators and associated
parameters. Since last four decades huge numbers of researchers have been
working on the performance of GA and its enhancement. This earlier research
work on analyzing the performance of GA enforces the need to further
investigate the exploration and exploitation characteristics and observe its
impact on the behavior and overall performance of GA. This paper introduces the
novel approach of adaptive twin probability associated with the advanced twin
operator that enhances the performance of GA. The design of the advanced twin
operator is extrapolated from the twin offspring birth due to single ovulation
in natural genetic systems as mentioned in the earlier works. The twin
probability of this operator is adaptively varied based on the fitness of best
individual thereby relieving the GA user from statically defining its value.
This novel approach of adaptive twin probability is experimented and tested on
the standard benchmark optimization test functions. The experimental results
show the increased accuracy in terms of the best individual and reduced
convergence time.Comment: 7 pages, International Journal of Advanced Studies in Computer
Science and Engineering (IJASCSE), Volume 2, Special Issue 2, 201
Focusing of timelike worldsheets in a theory of strings
An analysis of the generalised Raychaudhuri equations for string world sheets
is shown to lead to the notion of focusing of timelike worldsheets in the
classical Nambu-Goto theory of strings. The conditions under which such effects
can occur are obtained . Explicit solutions as well as the Cauchy initial value
problem are discussed. The results closely resemble their counterparts in the
theory of point particles which were obtained in the context of the analysis of
spacetime singularities in General Relativity many years ago.Comment: 14 pages, RevTex, no figures, extended, to appear in Phys Rev
Wave Equation for the Wu Black Hole
Wu black hole is the most general solution of maximally supersymmetric gauged
supergravity in D=5, containing gauge symmetry. We study the
separability of the massless Klein-Gordon equation and probe its singularities
for a general stationary, axisymmetric metric with orthogonal transitivity, and
apply the results to the Wu black hole solution. We start with the zero
azimuthal-angle eigenvalues in the scalar field Ansatz and find that the
residuum of a pole in the radial equation is associated with the surface
gravity calculated at this horizon. We then generalize our calculations to
nonzero azimuthal eigenvalues and probing each horizon singularity, we show
that the residua of the singularities for each horizon are in general
associated with a specific combination of the surface gravity and the angular
velocities at the associated horizon. It turns out that for the Wu black hole
both the radial and angular equations are general Heun's equations with four
regular singularities.Comment: 19 pages, minor corrections and reference added. Matches the
published versio
Killing(-Yano) Tensors in String Theory
We construct the Killing(-Yano) tensors for a large class of charged black
holes in higher dimensions and study general properties of such tensors, in
particular, their behavior under string dualities. Killing(-Yano) tensors
encode the symmetries beyond isometries, which lead to insights into dynamics
of particles and fields on a given geometry by providing a set of conserved
quantities. By analyzing the eigenvalues of the Killing tensor, we provide a
prescription for constructing several conserved quantities starting from a
single object, and we demonstrate that Killing tensors in higher dimensions are
always associated with ellipsoidal coordinates. We also determine the
transformations of the Killing(-Yano) tensors under string dualities, and find
the unique modification of the Killing-Yano equation consistent with these
symmetries. These results are used to construct the explicit form of the
Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of
dimensions and for its charged version.Comment: 87 pages. V2: typos are corrected, appendix C and references are
added. V3: several typos are fixe
The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
The present paper is both a review on the Feynman problem, and an original
research presentation on the relations between Fermionic theories and qubits
theories, both regarded in the novel framework of operational probabilistic
theories. The most relevant results about the Feynman problem of simulating
Fermions with qubits are reviewed, and in the light of the new original results
the problem is solved. The answer is twofold. On the computational side the two
theories are equivalent, as shown by Bravyi and Kitaev (Ann. Phys. 298.1
(2002): 210-226). On the operational side the quantum theory of qubits and the
quantum theory of Fermions are different, mostly in the notion of locality,
with striking consequences on entanglement. Thus the emulation does not respect
locality, as it was suspected by Feynman (Int. J. Theor. Phys. 21.6 (1982):
467-488).Comment: 46 pages, review about the "Feynman problem". Fixed many typo
Two-Qubit Separability Probabilities and Beta Functions
Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and
quant-ph/0304041), exact formulas are available (both in terms of the
Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and
(n(n-1)/2-1)-dimensional volumes of the complex and real n x n density
matrices. However, no comparable formulas are available for the volumes (and,
hence, probabilities) of various separable subsets of them. We seek to clarify
this situation for the Hilbert-Schmidt metric for the simplest possible case of
n=4, that is, the two-qubit systems. Making use of the density matrix (rho)
parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce
each of the real and complex volume problems to the calculation of a
one-dimensional integral, the single relevant variable being a certain ratio of
diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated
integrand in each case is the product of a known (highly oscillatory near nu=1)
jacobian and a certain unknown univariate function, which our extensive
numerical (quasi-Monte Carlo) computations indicate is very closely
proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2,
b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case.
Assuming the full applicability of these specific incomplete beta functions, we
undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and
reorganized, with the quasi-Monte Carlo integration sample size being greatly
increase
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