We consider the classes of functions of n variables which are intersections of the class M of monotone functions and other precomplete classes in three-valued logic. We find the asymptotic behaviour of the logarithm o...
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We consider the classes of functions of n variables which are intersections of the class M of monotone functions and other precomplete classes in three-valued logic. We find the asymptotic behaviour of the logarithm of cardinality of such classes as n -> infinity.
We propose a novel approach for generating test cases of software that includes mathematical functions, such as trigonometric functions, logarithmic functions, functions implemented as look-up tables with non-linear i...
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We propose a novel approach for generating test cases of software that includes mathematical functions, such as trigonometric functions, logarithmic functions, functions implemented as look-up tables with non-linear interpolation, and so on. A satisfiability modulo theories (SMT) solver is iteratively used to generate test cases in the scheme of bounded model checking. In the proposed method, mathematical functions are abstracted so that the derived formula can be easily treated using an SMT solver. The abstraction is refined adaptively based on the previous counterexamples. We also propose a general method to estimate an abstraction of a mathematical function by means of sampling and machine learning. Although the method proposed in this paper addresses mainly the topic of test-case generation, it is also applicable to ordinary bounded model checking under the assumption that the abstraction should be a correct over-approximation. We evaluated the proposed method by applying it to an example of embedded control software taken from the automotive industry. The experimental results show the usefulness of the proposed method.
We obtain the limit of the 2nth root (asymptotics of the logarithm) of the number of pseudo-Boolean functions of n variables that map adjacent vertices of the Boolean cube into adjacent vertices of an arbitrary graph,...
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Let f be a real meromorphic function of infinite order in the plane, with finitely many zeros and non-real poles. Then f '' has infinitely many non-real zeros.
Let f be a real meromorphic function of infinite order in the plane, with finitely many zeros and non-real poles. Then f '' has infinitely many non-real zeros.
We study the value-distribution of Dirichlet L-functions L(s, chi) in the half-plane sigma = (sic)s > 1/2. The main result is that a certain average related to the logarithm of L(s, chi) with respect to chi, or of ...
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We study the value-distribution of Dirichlet L-functions L(s, chi) in the half-plane sigma = (sic)s > 1/2. The main result is that a certain average related to the logarithm of L(s, chi) with respect to chi, or of the Riemann zeta-function zeta(s) with respect to (sic)s, can be expressed as an integral involving a density function, which depends only on sigma and can be explicitly constructed. Several mean-value estimates on L-functions are essentially used in the proof in the case 1/2 < sigma <= 1.
In this paper, we adopt the point of view of a decision-maker who evaluates a probabilistic model based on the test-sample averaged utility of the expected-utility optimal strategy that the model suggests in a horse r...
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In this paper, we adopt the point of view of a decision-maker who evaluates a probabilistic model based on the test-sample averaged utility of the expected-utility optimal strategy that the model suggests in a horse race setting. After briefly reviewing the basic properties of the resulting performance measure for probabilistic models, we show that such a measure ranks two models according to their likelihood ratio if and only if the performance measure is based on a generalized logarithmic utility function. Thus, we provide a new decision theoretic motivation of the likelihood ratio as a model performance measure.
Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g is an element of Hol(D) such that the sum vertical bar f vertic...
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Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g is an element of Hol(D) such that the sum vertical bar f vertical bar + vertical bar g vertical bar is equivalent to w. Also, we obtain similar results in several complex variables for circular, strictly convex domains with smooth boundary.
We investigate q-shift analogue of the lemma on logarithmic derivative of several variables. Let f be a meromorphic function in C-n of zero order such that f(0) not equal 0, infinity, and let q is an element of C-n\{0...
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We investigate q-shift analogue of the lemma on logarithmic derivative of several variables. Let f be a meromorphic function in C-n of zero order such that f(0) not equal 0, infinity, and let q is an element of C-n\logarithmic. Then we have m(r, f (qz)/f(z)) = o(T(r, f)) on a set of logarithmic density 1. The q-shift analogue of the first and the second main theorems of Nevanlinna theory of several variables and their applications is also shown..
This is the second of two papers devoted to the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Such a computation should enable a comparison with results from lattice simula...
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This is the second of two papers devoted to the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Such a computation should enable a comparison with results from lattice simulations in order to reveal the genuinely non-perturbative content of the latter. The gluon propagator is computed by means of Numerical Stochastic Perturbation Theory: results range from two up to four loops, depending on the different lattice sizes. The non-logarithmic constants for one, two and three loops are extrapolated to the lattice spacing a -> 0 continuum and infinite volume V -> infinity limits. (C) 2010 Elsevier B.V. All rights reserved.
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