可满足性问题的一种DNA表面计算模型

可满足性问题的一种DNA表面计算模型是一种特殊的DNA计算方法,该模型是采用荧光标记的策略和荧光猝灭技术,通过观察荧光灭光情况排除非解,从而有效的解决可满足性问题(SAT).该模型方法具有错误率低、编码简单、读取方便等很好的性能,能够大大减少实验过程中的错差.     

可满足实例的归结复杂度

GRB模型是一种随机约束满足问题模型,此模型具有精确的可满足相变现象。针对实验中出现的GRB模型在相变区域产生的可满足实例都是难解的现象,利用子句宽度和归结复杂度的关系证明了GRB模型在相变点附近产生的可满足实例对于树型归结证明具有指数下界。因此从理论上证明了在相变区域产生的可满足实例对基于归结的算法是难解的。     

基于扩展规则的模型计数与智能规划方法

提出命题扩展规则方法ER的一种高效实现.在此基础上,研究了扩展规则方法在3个领域的应用:提出一次性求解一系列相近SAT问题的快速算法nER;提出基于扩展规则的模型计数算法     

一个约束可满足性问题的演化算法求解

约束可满足性问题是一大类常出现于现实应用中的复杂问题,因其繁多的约束条件而出名。本文针对一个经典的约束可满足性问题——斑马属谁问题．基于演化算法的框架进行求解。我们采用矩阵的表示方式．并设计了相应的杂交和变异算予。实验表明．演化算法能高效地解决该问题。     

DNA自组装的可满足性问题模型

DNA自组装技术在DNA计算和纳米技术领域都发挥着极其重要的作用,许多小规模NP完全问题都可以通过自组装模型得以解决.文中以可满足问题为模型,通过构造范式中变量的特殊补链,使其与初始数据库中初始DNA链发生杂交反应,形成发夹结构,利用形成发夹结构的DNA链与没形成发夹结构的DNA链长度不同的特点,通过凝胶电泳将这些带发夹的DNA链提取出来;然后加入与这些特殊补链完全互补的DNA链,在一定温度下,通过碱基互补配对原则,发夹结构又将被重新打开.该模型充分利用了DNA分子间的自组装能力,在计算过程中只需要用到凝胶电泳操作,在一定程度上大大减少了因生物操作过多而引起的各种实验误差.     

采用二元CSP引擎求解RTL数据通路的可满足性

针对寄存器传输级(RTL)验证和测试过程中非常重要的数据通路可满足性求解问题,提出一种基于二元约束满足问题(CSP)的求解方法,包括数据通路提取、二元CSP建模和搜索求解3个步骤.数据通路提取通过对接口布尔变量和某些字变量赋值,为各个数据通路器件建立环境;二元CSP建模则根据该环境和各个数据通路器件的功能,将数据通路的可满足性问题转化为二元CSP描述;该二元CSP问题的描述被送入到二元CSP引擎,并采用冲突引导的回跳搜索策略进行求解,获得有解的例证或无解的判定.实验结果表明,即使在没有采取很多优化策略的条件下,该方法仍有较好的性能,并优于基于线性规划(LP)的求解方法.     

可满足问题的分子信标计算模型

分子信标（Molecular Beacon）是一种发夹状的荧光探针,它可以特异地和那些与分子信标的环（Loop）互补的核酸靶序列杂交,具有单个碱基错配的检测能力．肽核酸（Peptide Nucleic Acid）是人工合成的核酸（DNA）的类似物．PNA骨架为酰胺键,与DNA补链杂交更稳定,可以阻止聚合酶延伸反应．文中将可满足问题的约束变量编码于分子信标的环部识别区,通过分子信标与使得给定范式为真的变量的PNA补链杂交,再利用PNA链可以阻止聚合酶延伸反应的性质,用限制性内切酶EcoRI降解对应于非解的分子信标,最后通过加热表面使分子信标构形发生变化,产生荧光读解．提出的可满足问题的分子信标计算模型具有可靠性高、无需观察和记录计算的中间结果、读解简单等优点．     

基于DNA折纸术求解可满足性问题的计算模型

DNA折纸术是一种全新的DNA自组装方法,具有可编程性、纳米可寻址性等优点,被广泛地应用于DNA计算中.利用DNA折纸术可折叠出特殊结构的特点,在DNA折纸基底上设计了一种求解可满足性问题的计算模型,该模型采用分子信标原理,通过观察荧光的明灭排除非解,从而找出可满足性问题的解.最后通过实例和模拟仿真表明了模型的可行性.     

PSL可满足问题的计算复杂度

PSL是一种用于描述并行系统的属性规约语言,包括线性时序逻辑FL和分支时序逻辑OBE两部分。由于OBE就是CTL,因此论文重点研究FL逻辑。理论上已证明许多难解的问题都可多项式变换为“可满足性”问题,“可满足性”问题是研究时序逻辑的核心问题之一,并已成为程序验证的一种有力工具;而计算复杂度是“可满足性”问题需要解决的最深刻的方向之一,其研究意义在于它可作为解决一类问题的难度的标准。文中在利用“铺砖模型”基础上,推导并得出FL的“可满足性”问题的计算复杂度为EXPSPACE—hard,这对正确评价解决该问题的各种算法的效率,进而确定对已有算法的改进余地具有重要的指导意义。     

The satisfiability problem in regular CNF-formulas

 In this paper we deal with the propositional satisfiability (SAT) problem for a kind of multiple-valued clausal forms known as regular CNF-formulas and extend some known results from classical logic to this kind of formulas. We present a Davis–Putnam-style satisfiability checking procedure for regular CNF-formulas equipped with suitable data structures and prove its completeness. Then, we describe a series of experiments for regular random 3-SAT instances. We observe that, for the regular 3-SAT problem with this procedure, there exists a threshold of the ratio of clauses to variables such that (i) the most computationally difficult instances tend to be found near the threshold, (ii) there is a sharp transition from satisfiable to unsatisfiable instances at the threshold and (iii) the value of the threshold increases as the number of truth values considered increases. Instances in the hard part provide benchmarks for the evaluation of regular satisfiability solvers.     

Onk-positive satisfiability problem

An algorithm for solving the satisfiability problem is presented. It is proved that this algorithm solves 2-SAT and Horn-SAT in linear time andk-positive SAT (in which every clause contains at mostk positive literals) in timeO(|F|·ξ _n ^k ), where |F| is the length of inputF, n is the number of atoms occurring inF, and ξ _k is the greatest real number satisfying the equation . Compared with previous results, this nontrivial upper bound on time complexity could only be obtained fork-SAT, which is a subproblem ofk-positive SAT. Research partially supported by NSFC grant 221-4-1439. HUANG Xiong received his B.S. and M.S. degrees in computer science from Peking University in 1992 and 1995 respectively. Now he is a Ph.D. candidate in Beijing University of Aeronautics and Astronautics. His major research interests are design and analysis of algorithms, computational complexity, and satisfiability problem. LI Wei received his B.S. degree in mathematics from Peking University in 1966 and his Ph.D. degree in computer science from The University of Edinburgh in 1983. Since 1986, he has been a Professor in computer science at Beijing University of Aeronautics and Astronautics. He has published over 100 papers in the areas of concurrent programming languages, operational semantics, type theory, and logical foundation of artificial intelligence.     

求解多文字可满足SAT问题的置信传播算法

可满足(SAT)问题是指:是否存在一组布尔变元赋值,使得合取范式公式中每个子句至少有一个文字为真.多文字可满足SAT问题是指:是否存在一组布尔变元赋值,使得CNF公式中每个子句至少有两个文字为真.显然,此问题仍然是一个NP难问题.为了研究解决多文字可满足SAT问题的算法,引入随机实例产生模型,设计求解多文字可满足SAT问题的置信传播算法.最后,用实例模型产生了大量数据进行实验验证,结果表明:该算法求解多文字可满足SAT问题的性能优于其他启发式算法.     

多文字可满足SAT问题的相变点上界

可满足(SAT)问题是指：是否存在一组布尔变元赋值,使得随机合取范式(CNF)公式中每个子句至少有1个文字为真。多文字可满足SAT问题是指：是否存在一组布尔变元赋值,使得随机CNF公式中每个子句至少有2个文字为真。此问题仍然是一个NP难问题。定义约束密度α为CNF公式子句数与变元数之比,对该问题的相变点上界α^*进行了研究。如果α>α^*,则多文字可满足SAT问题高概率不可满足。通过一阶矩一个简单的推断,可以证明α^*=-ln 2/ln(1-(k+1)/2^k),当k=3时,α^*=1。利用Kirousis等人的局部最大值技术,提升了多文字可满足3-SAT问题的相变点上界α^*=0.7193。最后,选择了大量数据进行实验验证,结果表明,理论结果与实验结果相吻合。     

Interactive scheduling as a constraint satisfiability problem

A constraint satisfiability problem consists of a set of variables, their associated domains (i.e., the set of values the variable can take) and a set of constraints on these variables. A solution to the CSP is an instantiation (or labeling) of all the variables which does not violate any of the constraints. Since constraint satisfiability problems are, in general, NP-complete, it is of interest to compare the effectiveness and efficiency of heuristic algorithms as applied, in particular, to our application. Our research effort attempts to determine which algorithms perform best in solving the student scheduling problem (SSP) and under what conditions. We also investigate the probabilistic techniques of Nudel for finding a near-optimal instantiation order for search algorithms, and develop our own modifications which can yield a significant improvement in efficiency for the SSP. Experimental results have been collected and are reported here. Our system was developed for and used at Bar-Ilan University during the registration period, being available for students to construct their timetables.     

约束可满足性中求解RB模型实例的算法综述

约束满足问题是人工智能领域中最基本的NP完全问题之一。多年来,随着约束满足问题的深入研究,国内外学者提出多种实例模型。其中,RB模型是一种能生成具有精确相变的增长域约束满足问题实例,其求解难度极具挑战性。为了寻找其求解的新型高效算法,促进约束可满足问题的RB模型求解算法领域的研究,首先从约束满足问题的模型发展、求解技术进行分析;其次,对各类求解RB模型实例算法进行梳理,将求解的算法文献划分为回溯启发式类、信息传播类和元启发式类相关改进算法,从算法原理、改进策略、收敛性和精确度等方面进行对比综述;最后给出求解RB模型实例算法的研究趋势和发展方向。     

Bee colony optimization for the satisfiability problem in probabilistic logic

This paper presents the first heuristic method for solving the satisfiability problem in the logic with approximate conditional probabilities. This logic is very suitable for representing and reasoning with uncertain knowledge and for modeling default reasoning. The solution space consists of variables, which are arrays of 0 and 1 and the associated probabilities. These probabilities belong to a recursive non-Archimedean Hardy field which contains all rational functions of a fixed positive infinitesimal. Our method is based on the bee colony optimizationmeta-heuristic. The proposed procedure chooses variables from the solution space and determines their probabilities combining some other fast heuristics for solving the obtained linear system of inequalities. Experimental evaluation shows a high percentage of success in proving the satisfiability of randomly generated formulas. We have also showed great advantage in using a heuristic approach compared to standard linear solver.     

On optimizing the satisfiability (SAT) problem

1IntroductionThesatisfiability(SAT)problemistodeterminewhetherthereexistsanassignmentofvaluesin{0,1}toasetofBooleanvariables{x1,xm}thatmakesaconjunctivenormalform(CNF)formulatrue.ThesatisfiabilityproblemofaCNFformulawithatmostlliteralsineachclauseiscalledthel-SATproblem.Theoretically,for>3,theSATproblemisawell-knownNP-completeproblem.Andthus,thereexistsnopolynomialtimealgorithmfortheSATproblemontheassumptionthatPNP.Ontheotherhand,theSATproblemisfundamentalinsolvingmanypracticalprob…