相关论文: Analysis of Boolean Functions
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
A survey of general results on the singularities of inverses to meromorphic functions is given, with applications to holomorphic dynamics. This is a lecture delivered at the workshop "The role of complex analysis in complex dynamics" in…
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…
Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
Lecture 1 discusses non-Archimedean analogs of classical complex function theory based on the Schnirelman integral. Lecture 2 discusses valuation (Newton) polygons and their consequences and presents a non-Archimedean analog of the…
Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…
We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach.…
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized…
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to…
Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and…
In the present note we prove an asymptotically tight relation between additive and multiplicative complexity of Boolean functions with respect to implementation by circuits over the basis {+,*,1}.
In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…
This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…
This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…