Congruences and ideals in pseudoeffect algebras

This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~ _I induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~ _I induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~ _I is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I = [0]_~ is a normal weak Riesz ideal, and ~ _I = ~. This work was supported by the National Natural Science Foundation of China (Grant No. 10271069).     

Problems on mathematical safes on graphs

For given two sets of locks, the corresponding problems on mathematical safes are formulated on graphs. In the first set, all the locks have the same number of sates and, in the second set, any pair of locks can consist of different numbers of sates. A number of conditions are obtained under which there exist solutions to these problems for safes specified on directed or undirected single graphs such as a path, a chain, a cycle, and a star. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 14–21, September–October 2006.     

剩余格的T-模糊滤子与T-模糊同余关系

将t-模应用于模糊滤子和模糊同余上,引入剩余格的T-模糊滤子与T-模糊同余,并分别研究T-模糊滤子与T-模糊同余的性质与一些等价刻画;得到全体T-模糊滤子的集合与T-模糊同余的集合是同构;研究了由T-模糊滤子所诱导的商剩余格以及同态定理。这些理论在其他的逻辑代数系统仍然成立。     

Parametric synchronizations in mobile nominal calculi

We present and compare P-PRISMA and F-PRISMA, two parametric calculi that can be instantiated with different interaction policies, defined as synchronization algebras with mobility of names (SAMs). In particular, P-PRISMA is based on name transmission (P-SAM), like π-calculus, and thus exploits directional (input–output) communication only, while F-PRISMA is based on name fusion (F-SAM), like Fusion calculus, and thus exploits a more symmetric form of communication. However, P-PRISMA and F-PRISMA can easily accommodate many other high-level synchronization mechanisms than the basic ones available in π-calculus and Fusion, hence allowing for the development of a general meta-theory of mobile calculi. We define for both the labeled operational semantics and a form of strong bisimilarity, showing that the latter is compositional for any SAM. We also discuss reduction semantics and weak bisimilarity. We give several examples based on heterogeneous SAMs, we investigate the case studies of π-calculus and Fusion calculus giving correspondence theorems, and we show how P-PRISMA can be encoded in F-PRISMA. Finally, we show that basic categorical tools can help to relate and to compose SAMs and PRISMA processes in an elegant way.     

移动界程演算理论及应用研究综述

移动界程演算通过界程这一核心概念来表达有边界的计算场所,并提供界程移动,认证和授权等能力从最基础层次刻画移动计算的本质,成为了移动计算系统形式化理论和应用领域内的重要研究分支。对移动界程演算的理论及应用方面的研究和发展进行了概述,对移动界演算的扩展语义和代数性质的分析方法、移动界演算的空间逻辑和模型检测算法以及移动界程在计算系统建模方面应用现状进行了整理和分析,并对该领域未来进一步研究的方向进行了展望。     

A Congruence for Petri Nets

We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs.     

Factor congruences in BCK-algebras

In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop residuation algebras and its subvarieties. We prove that free algebras in a non k-potent subvariety of are indecomposable while finitely generated free algebras in k-potent subvarieties have a unique non-trivial decomposition into a direct product of two factors, and one of them is the two-element implication algebra. This paper is partially supported by Universidad Nacional del Sur and CONICET.     

一类格值自动机的极小化

给出了格值自动机的同余和同态,从代数角度出发详细研究了同余和同态关系的代数性质,揭示了格值自动机的代数性质和取值格半群的紧密联系,利用同余和同态关系最终研究了格值自动机的极小化问题,在正则同余下给出了可在有限步实现具有模糊初始状态和特殊模糊终状态的自动机极小化的算法。     

A strongly primitive word of arbitrary length and its application †

It is known that both the class of all (n,k)-languages and the class of all time-variant languages over a finite alphabet contain the class of all regular languages. In this paper we show that in general neither one of these two classes of languages contains the other by constructing an infinite sequence of strongly primitive words over an alphabet with four letters.     

基于线性同余的IDMA交织器设计及分析

本文提出了一种新的基于线性同余的IDMA交织器设计方案, 并且给出了详细的交织器设计算法. 它能满足IDMA交织器设计中低存储量、容易产生交织序列、交织器同步数据少、交织器之间相关性小的要求. 本文的仿真结果证明了这种交织器性能优于伪随机交织器。