Generating cryptographically strong Boolean functions using partial information

Periodica Mathematica Hungarica - In our paper we study the usage of partially defined Boolean functions (PDBFs) for generating cryptographically strong Boolean functions. A PDBF can be considered...     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

关于可达矩阵的求法探讨

在《离散数学》、《图论》课程中 ,用矩阵表示图时 ,涉及到一类重要的矩阵——可达矩阵 ,它是判别图中任意两点是否有通路的重要手段 ,也是求强分图的重要方法 ,但是可达矩阵的求法比较复杂 .本文针对这一问题 ,对可达矩阵的求法进行了改进 ,提出了一种简单可行的算法 .     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

On a Boolean-valued Model of the Strict Implication System(Continuous)

The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5.     

无原子布氏代数理论的计算复杂性

研究无原子布氏代数的计算复杂性 .得到了下面的新定理 :定理 1　无原子布氏代数理论Δ具有完全的量词消去法 ,也就是说每一个式子都Δ等价于一个开式子 .定理 2　无原子布氏代数的初等型Γ (x1,… ,xn)是由型内的不含量词的全体开式子所唯一决定 .定理 3　无原子布氏代数的一个长度为 n的语句的判断过程所消耗的 Turing时间和空间都是属于 2 2 cn指数级 .     

布尔“复合函数”的Walsh循环谱和自相关函数

本文利用布尔随机变量联合分布的分解式给出了布尔“复合函数”和某布尔函数符合率的分解算式,由此求得了布尔“复合函数”的 Walsh循环谱和自相关函数的计算公式,公式清楚地表明了“复合”所得布尔函数的 Walsh循环谱与起“复合”作用的函数和被“复合”的各函数所有线性组合的 Walsh循环谱之间的关系、“复合”所得布尔函数的自相关函数与起“复合”作用的函数谱和被“复合”的各函数的谱及相关函数之间的关系,这两个公式在布尔函数的密码学性质研究中会有广泛的应用.     

Representation of Hilbert algebras and implicative semilattices

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.     

逻辑函数在布尔减-异或、布尔除-符合代数系统中的规范展开式

证明了布尔减、异或运算以及布尔除、符合运算的完备性,并从与-异或及或-符合代数系统中的RM、CRM展开式出发,分别推导了任意逻辑函数在布尔减-异或及布尔除-符合代数系统中的规范展开式.举例说明了与-或-非代数系统中规范展开式与布尔减-异或、布尔除-符合代数系统中的规范展开式之间的转换.     

有向全图的幂敛指数和周期

设G是有向图,T(G)表示G的有向全图.本文得到了它们的幂敛指数k(G)和k(T)之间的关系:对任何有向图G,周期p(T(G))=1;当G是本原图时,k(T)≤k(G)+1,文中给出了取得k(G)+1的两类图;当G是无圈图时,k(T)=2k(G)-1,当G是有向圈时,k(T)=2|V(G)|-1,当G是强连通时得到了k(T)的一些估计.