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.     

单亲遗传算法图式定理的进一步分析

图式定理是遗传算法的重要理论基础之一。本文对单亲遗传算法的图式定理进行了全面的分析研究,给出了单亲遗传算法图法定理的表达式,并对各种遗传算子破坏图式的概率作了估算。     

Connected sum of digital closed surfaces

During the past 20 years the research of digital surfaces has proceeded to find their properties in the digital space Zⁿ, such as a topological number, a simple k-point, the 3D-Jordan theorem, a k-separating set, a boundary detecting algorithm and so on. Actually, unlike surfaces in a continuous space, the features of digital surfaces have different characteristics. The aim of this paper is to introduce the notion of a digital closed k-surface in Zⁿ, n ? 3, with the general k-adjacency relations as a generalization of Malgouyres’ and Morgenthaler’s k-surfaces in Z³, to establish some minimal simple closed k-surfaces in Z³ and to find their digital topological properties in relation with the k-fundamental group and k-contractibility. Moreover, a connected sum of two digital closed surfaces is introduced and its digital topological properties are investigated.     

Parallelization of a Hyper-Linking–Based Theorem Prover

We describe the parallelization of a first-order logic theorem prover that is based on the hyper-linking proof procedure (HLPP). Four parallel schemes – process level, clause level, literal level, and flow level – are developed for two types of sequential implementation of HLPP: list based and network based. The motivation for developing each parallel scheme is presented, and the architecture and implementation details of each scheme are described. Issues about parallel processing, such as serialization and synchronization, load balancing, and access conflicts, are examined. Speedups over sequential implementations are attained, and timing results for benchmark problems are provided.     

Experimenting with Isabelle in ZF set theory

The theorem prover Isabelle has been used to axiomatise ZF set theory with natural deduction and to prove a number of theorems concerning functions. In particular, the well-founded recursion theorem has been derived, allowing the definition of functions over recursive types (such as the length and the append functions for lists). The theory of functions has been developed sufficiently within ZF to include PP, the theory of continuous functions forming the basis of LCF. Most of the theorems have been derived using backward proofs, with a small amount of automation.The work has been carried out at the Computer Laboratory of the University of Cambridge.     

What holds in a context?

In order to establish that [A] = [B] follows from a set of assumptions often one provesA =B and then invokes the principle of substitution of equals for equals. It has been observed that in the ancillary proof ofA =B one is allowed to use, in addition to those assumptions of which are free for , certain (open) sentencesP which may not be part of and may not follow from , but are related to the context . We show that in an appropriate formal system there is a closed form solution to the problem of determining precisely what sentencesP can be used. We say that those sentenceshold in the context under the set of assumptions . We suggest how the solution could be exploited in an interactive theorem prover.     

基于心态指标的区间灰数关联度模型

针对已有的灰色关联度模型仅适用于实数序列而不能应用于区间灰数序列的情况,通过引入决策者心态指标,将区间灰数序列转化为决策者心态指标序列,并且当决策者的心态指标确定时,心态指标序列就转化为实数序列,于是通过对体现决策者心态的实数序列建立灰色关联度模型,得到了反映出决策者心态的灰色关联度,从而构建了基于心态指标的区间灰数关联度模型。决策者处于不同心态时,可以通过调整其心态计算灰关联度,从而使建立的关联度模型更加符合实际。最后,通过计算实例说明了模型的可行性。     

有关中国剩余定理在多个素数的RSA解密运算中的加速公式的论证以及加速效率的估算

RSA算法在公钥密码体制中占有重要的地位,它的计算效率与模幂运算的实现效率有着直接关联。本实验在基于使用中国剩余定理简化的RSA解密算法的条件下,给出多个素数情况下的解密通用公式,通过减少大量的模幂运算,迅速简单地恢复出原文。并给出了效率提升估算公式,通过估算求出加速效率,为确定使用多少个素数最为合适提供依据。