Espaces métriques rationnellement présentés et complexité, le cas de l'espace des fonctions réelles uniformément continues sur un intervalle compact

We define the notion of rational presentation of a complete metric space, in order to study metric spaces from the algorithmic complexity point of view. In this setting, we study some representations of the space C[0,1] of uniformly continuous real functions over [0,1] with the usual norm: ||f||_∞ = Sup{|f(x)|; 0x1}. This allows us to have a comparison of global kind between complexity notions attached to these presentations. In particular, we get a generalization of Hoover's results concerning the Weierstrass approximation theorem in polynomial time. We get also a generalization of previous results on analytic functions which are computable in polynomial time.     

线性关联规则研究

首先讨论了布尔型关联规则的不足,然后提出了线性关联规则的概念,详细讨论了线性关联规则的挖掘方法,具体给出了线性关联规则的挖掘过程,分析了线性关联规则的作用。还给出了实验结果,并将线性关联规则和布尔型关联规则及定量关联规则进行了比较。     

Free binary decision diagrams for the computation of EAR n

Free binary decision diagrams (FBDDs) are graph-based data structures representing Boolean functions with the constraint (additional to binary decision diagram) that each variable is tested at most once during the computation. The function EAR_n is the following Boolean function defined for n × n Boolean matrices: EAR_n(M) = 1 iff the matrix M contains two equal adjacent rows. We prove that each FBDD computing EAR_n has size at least and we present a construction of such diagrams of size approximately .     

Distributed computing on oriented anonymous hypercubes with faulty components

We give efficient algorithms for distributed computation on oriented, anonymous, asynchronous hypercubes with possible faulty components (i.e. processors and links) and deterministic processors. Initially, the processors know only the size of the network and that they are inter-connected in a hypercube topology. Faults may occur only before the start of the computation (and that despite this the hypercube remains a connected network). However, the processors do not know where these faults are located. As a measure of complexity we use the total number of bits transmitted during the execution of the algorithm and we concentrate on giving algorithms that will minimize this number of bits. The main result of this paper is an algorithm for computing Boolean functions on anonymous hypercubes with bit cost , where is the number of faulty components (i.e. links plus processors), is the number of links which are either faulty, or non-faulty but adjacent to faulty processors, and is the diameter of the hypercube with faulty components. Received: October 1992 / Accepted: April 2001     

Elimination of Boolean variables for probabilistic coherence

 In this paper we deal with the computational complexity problem of checking the coherence of a partial probability assessment (called CPA). The CPA problem, like its analogous PSAT, is NP-complete so we look for an heuristic procedure to make tractable reasonable instances of the problem. Starting from the characteristic feature of de Finetti's approach (i.e. the explicit distinction between the probabilistic assessment and the logical relations among the sentences) we introduce several rules for a sequential “elimination” of Boolean variables from the domain of the assessment. The procedure resembles the well-known Davis-Putnam rules for the satisfiability, however we have, as a drawback, the introduction of constraints (among real variables) whose satisfiability must be checked. In simple examples we test the efficiency of the procedure respect to the “traditional” approach of solving a linear system with a huge coefficient matrix built from the atoms generated by the domain of the assessment.     

对称密码算法S盒安全性分析

S盒是大多数对称密码算法中唯一的非线性结构,其密码学特性直接决定了密码算法的好坏。该文对美国高级加密标准 AES 算法、韩国对称加密标准SEED算法、欧洲对称加密标准 Camellia算法和中国商用密码标准SMS4算法的S盒密码学性质进行了深入的探讨,研究各种算法中S盒的代数性质和布尔函数性质,分析各种算法抵抗差分密码分析和线性密码分析等攻击的能力。通过对比S盒的优缺点,揭示了各种算法的安全性。     

Weak Schur numbers and the search for G.W. Walker’s lost partitions

A set A of integers is weakly sum-free if it contains no three distinct elements x,y,z such that x+y=z. Given k≥1, let WS(k) denote the largest integer n for which {1,…,n} admits a partition into k weakly sum-free subsets. In 1952, G.W. Walker claimed the value WS(5)=196, without proof. Here we show WS(5)≥196, by constructing a partition of {1,…,196} of the required type. It remains as an open problem to prove the equality. With an analogous construction for k=6, we obtain WS(6)≥572. Our approach involves translating the construction problem into a Boolean satisfiability problem, which can then be handled by a SAT solver.     

Construction of 1-resilient Boolean functions with optimum algebraic immunity

In this paper, for an integer n≥10, two classes of n-variable Boolean functions with optimum algebraic immunity (AI) are constructed, and their nonlinearities are also determined. Based on non-degenerate linear transforms to the proposed functions, we can obtain 1-resilient n-variable Boolean functions with optimum AI and high nonlinearity if n?1 is never equal to any power of 2.     

Updating method for the computation of orbits in parallel and sequential dynamical systems

In this article, we provide a matrix method in order to compute orbits of parallel and sequential dynamical systems on Boolean functions. In this sense, we develop algorithms for systems defined over directed (and undirected) graphs when the evolution operator is a general minterm or maxterm and, likewise, when it is constituted by independent local Boolean functions, so providing a new tool for the study of orbits of these dynamical systems.