关于同步部分规约的有限自动机的优化问题的近似难度

自动机是可同步的是指它具有满足以下性质的同步字:不论自动机当前所处的状态,以同步字为输入执行后它一定会到达某个特定状态。同步自动机问题的核心是计算最短同步字。聚焦于这一核心问题,文中就一类称为部分规约的确定的有限自动机的最短同步字问题,研究了近似计算这类自动机的最短同步字的复杂性,即近似计算它的难度,该工作有助于其近似算法的分析与设计。通过建立由两个优化问题(MAX SAT问题以及MAX FA-INT问题)到最短同步字长度计算这一问题(即Shortest-Syn)的归约,利用与概率可检验证明(Probabilistically Checkable Proofs,PCP)定理和概率可检验辩论(Probabilistically Checkable Debate,PCD)定理有关的若干结果证明了文中的主要结论:对于部分规约的确定的有限自动机,在某个近似因子内Shortest-Syn的近似难度是NP-难的和PSPACE-难的,除非NP和PSPACE分别坍塌到P。     

The derivation of on-line algorithms,with an application to finding palindromes

A theory for the derivation of on-line algorithms is presented. The algorithms are derived in the Bird-Meertens calculus for program transformations. This calculus provides a concise functional notation for algorithms, and a few powerful theorems for proving equalities of functions. The theory for the derivation of on-line algorithms is illustrated with the derivation of an algorithm for finding palindromes.An on-line linear-time random access machine (RAM) algorithm for finding the longest palindromic substring in a string is derived. For the purpose of finding the longest palindromic substring, all maximal palindromic substrings are computed. The list of maximal palindromes obtained in the computation of the longest palindrome can be used for other purposes such as finding the largest palindromic rectangle in a matrix and finding the shortest partition of a string into palindromes.This research was supported by the Dutch organization for scientific research NWO, under NFI project STOP, project number NF 62/63-518.     

Synchronizing generalized monotonic automata

In an earlier paper, we have studied reset words for synchronizing automata whose states admit a stable linear order. Here we show that the same bound on the length of the shortest reset word persists for synchronizing automata satisfying much weaker stability restriction. This result supports our conjecture concerning the length of reset words for synchronizing automata accepting only star-free languages.     

拟陷阱同步自动机的最短同步字的长度

既非陷阱也非强连通的同步自动机称为拟陷阱同步自动机。对于任意的拟陷阱同步自动机A,利用其强连 通子自动机的状态数给出了A的最短同步字的长度的一个上界,进而获得了A满足Lcrny猜想的一个充分条件。     

On synchronizing unambiguous automata

We give a polynomial upper bound for the length of the shortest word of minimal rank in a transitive n-state unambiguous automation whose transition monoid does not contain the null relation. In particular, in an n-state synchronizing unambiguous automation there is a synchronizing word of length less than .     

An Artificial Immune System Heuristic for Generating Short Addition Chains

This paper deals with the optimal computation of finite field exponentiation, which is a well-studied problem with many important applications in the areas of error-correcting codes and cryptography. It has been shown that the optimal computation of finite field exponentiation is a problem which is closely related to finding a suitable addition chain with the shortest possible length. However, it is also known that obtaining the shortest addition chain for a given arbitrary exponent is an NP-hard problem. As a consequence, heuristics are an obvious choice to compute field exponentiation with a semi-optimal number of underlying arithmetic operations. In this paper, we propose the use of an artificial immune system to tackle this problem. Particularly, we study the problem of finding both the shortest addition chains for exponents e with moderate size (i.e., with a length of less than 20 bits), and for the huge exponents typically adopted in cryptographic applications, (i.e., in the range from 128 to 2048 bits).     

计算最短公共超串的贪婪算法

最短公共超串问题就是对给定的子串集合找到包含每个子串的可能的串.这个问题是一个NP-完全问题.目前已有一些方法对此进行了研究.通过对各子串的分析和研究,提出了一种近似于贪婪算法的求最短公共超串问题算法,该算法可应用于解决DNA片段组装和数据压缩问题.最后给出了几个实例.     

互联网络RCP（n）的最短路算法

RCP（n）是最近提出的一种新型互联网络拓扑结构,是由环、Petersen图和交叉立方体所组成的,具有短直径、良好的可扩展性和正则性以及较小的构造开销的性质,是一种具有良好拓扑性质的互联网络。针对RCP（n）上节点编码的特点,采用逐步分解编码,依次寻找路径的方法给出了寻找RCP（n）上任意两点间最短路的一个多项式算法,为RCP（n）上作进一步的路由算法、最优分组等通讯性能的研究提供了理论支持,因此具有一定的理论意义和应用价值。     

基于两层编码遗传算法的机器人路径规划

讨论了在障碍物已知的二维环境里,在两上已知点之间寻找最短欧氏路径的问题,用了一种基于遗传算法的新的空间分割的方法,在遗传算法中,提出了一种新的编码方法－两层编码,这种编码来源于分子数量遗传学中的遗传机制,它能够大大夺强编码的表达能力,这种方法的核心就在于通过中间层编码来降低搜索的复杂度。     

Sophistication Revisited

Kolmogorov complexity measures the amount of information in a string as the size of the shortest program that computes the string. The Kolmogorov structure function divides the smallest program producing a string in two parts: the useful information present in the string, called sophistication if based on total functions, and the remaining accidental information. We formalize a connection between sophistication (due to Koppel) and a variation of computational depth (intuitively the useful or nonrandom information in a string), prove the existence of strings with maximum sophistication and show that they are the deepest of all strings.     

A probabilistic model to evaluate computer software piracy

The growing occurrence of computer software piracy has led to a new area of research, i.e., the development of methods to be used to supply evidence that software was copied.One method to argue that computer source code was copied is to examine the occurence of strings of binary code (ones and zeroes) between the alleged parent and pirate codes. Given the occurence of a lengthy identical string between codes, and that string represents a development of executable code (versus data blocks that can be argued to exist in only one fashion), a model of the probability of repetition of such a string of code occurring between so-called independently derived source codes can be formulated. The developed probabilistic results can also be approximately by a simpler formula derived herein. A computer program and example computations are presented.     

互联网络RCP(n)的最短路算法

RCP(n)是最近提出的一种新型互联网络拓扑结构,是由环、Petersen图和交叉立方体所组成的,具有短直径、良好的可扩展性和正则性以及较小的构造开销的性质,是一种具有良好拓扑性质的互联网络.针对RCP(n)上节点编码的特点,采用逐步分解编码,依次寻找路径的方法给出了寻找RCP(n)上任意两点间最短路的一个多项式算法,为RCP(n)上作进一步的路由算法、最优分组等通讯性能的研究提供了理论支持,因此具有一定的理论意义和应用价值.     

基于ITS的加速最短路径搜索算法研究

文章从路径搜索的基本原理入手,首先介绍了经典Dijkstra最短路径搜索算法,分析比较了基于堆结构和基数堆结构的Dijkstra算法的搜索效率,从而提出了采用多层地图和分级搜索技术来实现对最短路径搜索空间的控制策略和算法,结合湛江市区电子地图进行对比实验,该算法有效地解决了最短路径搜索效率的问题。     

On-line construction of parameterized suffix trees for large alphabets

We consider on-line construction of the suffix tree for a parameterized string, where we always have the suffix tree of the input string read so far. This situation often arises from source code management systems where, for example, a source code repository is gradually increasing in its size as users commit new codes into the repository day by day. We present an on-line algorithm which constructs a parameterized suffix tree in randomized O(n) time, where n is the length of the input string. Our algorithm is the first randomized linear time algorithm for the on-line construction problem.     

无存贮音码汉字字符串的音码反查实现技术

该文用无存贮音码汉字字符串的音码反查实现技术,解决以往汉字型字符串在通过首音码或拼音全码进行反查时需要事先存贮汉字型字符串的音码作为辅助记忆码;解决一个汉字型字符串在转换音码时产生多个编码时需要选择问题;解决一个汉字型字符串由于转换时重码选择建立者与使用者的歧义问题。该文在GBK汉字库范围内,以首音码为例,使用汉字首音码库作为字典,实现无存贮音码汉字字符串的音码反查实现技术。     

A distributed shortest path algorithm for a planar network

An algorithm is presented for finding a single source shortest path tree in a planar undirected distributed network with nonnegative edge costs. The number of messages used by the algorithm is O(n^5/3) on an n-node network. Distributed algorithms are also presented for finding a breath-first spanning tree in general network, for finding a shortest path tree in a general network, for finding a separator of a planar network, and for finding a division of a planar network.     

Effective synchronizing algorithms

The notion of a synchronizing sequence plays an important role in the model-based testing of reactive systems, such as sequential circuits or communication protocols. The main problem in this approach is to find the shortest possible sequence which synchronizes the automaton being a model of the system under test. This can be done with a synchronizing algorithm. In this paper we analyze the synchronizing algorithms described in the literature, both exact (with exponential runtime) and greedy (polynomial). We investigate the implementation of the exact algorithm and show how this implementation can be optimized by use of some efficient data structures. We also propose a new greedy algorithm, which relies on some new heuristics. We compare our algorithms with the existing ones, with respect to both runtime and quality aspect.     

Prioritizing test cases with string distances

Test case prioritisation aims at finding an ordering which enhances a certain property of an ordered test suite. Traditional techniques rely on the availability of code or a specification of the program under test. We propose to use string distances on the text of test cases for their comparison and elaborate a prioritisation algorithm. Such a prioritisation does not require code or a specification and can be useful for initial testing and in cases when code is difficult to instrument. In this paper, we also report on experiments performed on the “Siemens Test Suite”, where the proposed prioritisation technique was compared with random permutations and four classical string distance metrics were evaluated. The obtained results, confirmed by a statistical analysis, indicate that prioritisation based on string distances is more efficient in finding defects than random ordering of the test suite: the test suites prioritized using string distances are more efficient in detecting the strongest mutants, and, on average, have a better APFD than randomly ordered test suites. The results suggest that string distances can be used for prioritisation purposes, and Manhattan distance could be the best choice.     

枚举有符号基因组的可行交互移位算法

交互移位排序问题(SRT)是寻找一个使一个基因组转变为另一个基因组的最短交互移位序列。现在已有多个多项式时间的SRT算法,但大多数问题实例都有许多个最短交互移位序列,因此寻找所有最短交互移位序列问题是SRT一个自然的推广。这个问题可以归约为寻找一个基因组相对于另一个基因组的全部可行交互移位,即所有移位ρ满足:在一个基因组上执行ρ之后,所得基因组相对于另一个基因组的移位距离会减少。本文提出一个用来寻找全部可行交互移位的有效算法,尽管新算法的时间复杂度比穷举法改进不大,但实验结果表明,其在实际运行中表现更好。