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。     

PSL构造双向交换自动机及非确定自动机的方法

PSL(property specification language)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(foundation language)和分支时序逻辑OBE(optional branching extension)两部分.由于OBE就是CTL(computation tree logic),并且具有时钟声明的公式很容易改写成非时钟公式,因此重点研究了非时钟FL逻辑.为便于进行模型检验,每个FL公式必须转化成为一种可验证形式,通常是自动机(非确定自动机).构造非确定自动机的过程主要是通过中间构建交换自动机来实现.详细给出了由非时钟FL构造双向交换自动机的构造规则.构造规则的核心逻辑不仅仅局限于是在LTL(linear temporal logic)基础上的正规表达式,而且全面而充分地考虑了各种FL操作算子的可能性.并且给出了将双向交换自动机转化为非确定自动机的一种方法.最后,编写了将PSL转化为上述自动机的实现工具.FL双向交换自动机的构造规则计算复杂度仅是FL公式长度的线性表达式,验证了构造规则的正确性.在此基础上,证明了双向交换自动机与其转化的等价的非确定自动机接受的语言相同.上述工作对解决复杂并行系统建模和模型验证问题具有重要的理论意义和应用价值.     

相似时间序列的快速检索算法

在前人提出的扩展时序数据距离定义的基础上 ,首先提出一种在时域上计算时序数据距离的新算法 ,该算法时间复杂度为 O( n× m ) ,能够解决时序数据在 Y轴上的漂移和伸缩带来的问题 ;之后提出一种在频域上计算时序数据距离的新算法 ,该算法时间复杂度仅为 O( n× fc) ,效率很高 ,便于在线实现 ,而且同样能够解决时序数据漂移和伸缩的问题 ;本文还给出和证明了该算法的一个重要组成部分 :时序数据增量式的 DFT算法     

分支时态描述逻辑ALC-CTL及其可满足性判定

时态描述逻辑是将描述逻辑与时态逻辑相结合后得到的逻辑系统,具有较强的描述能力;但是大部分的时态描述逻辑都是将时态算子同时引入到概念和公式中,使得公式可满足性问题的计算复杂度过高。将描述逻辑ALC与分支时态逻辑CTL相结合,提出新的分支时态描述逻辑ALC-CTL。该逻辑没有将时态算子用于概念的构造过程,而是将时态算子引入到公式的构造中;从分支时态逻辑的角度看,相当于将CTL中的原子命题提升为描述逻辑中的个体断言。最终得到的逻辑系统不仅具有较强的刻画能力,还使得公式可满足性问题的复杂度保持在EXPTIME-完全这个级别。通过将CTL的Tableau判定算法与描述逻辑ALC的推理机制有机结合,给出了ALC-CTL的Tableau判定算法并证明了算法的可终止性、可靠性和完备性。     

时间区间时序逻辑的判定性与表达能力

模型检测技术在实时系统验证中被广泛使用。离散时间区间时序逻辑满足性是可判定的,因而也是可模型检测的。连续时间域时间区间时序逻辑是否可模型检测,则并不清楚。约束时间域到非负实数,证明了其可满足性是不可判定的,但存在该逻辑的可判定子集,并发现了这样的子集。由于模型检测问题可归约为时序逻辑满足性判定问题,因此结果表明,时间区间时序逻辑不可模型检测,但其可判定子集可模型检测。     

描述逻辑FL0循环术语集的可满足性

循环术语集是描述逻辑长期以来的研究难点,它的最基本的问题即语义及推理问题没有得到合理的解决。分析了描述逻辑循环术语集的研究现状和存在的问题,基于图的互模拟的方法,给出了描述逻辑FL0循环术语集的可满足性条件。结果证明循环术语集的可满足性的推理是多项式复杂的。     

带测试动作的动态时序逻辑扩展

作为一种动态知识表示形式,动态时序逻辑(DLTL)尤适用于正规程序验证,然而它不直接支持测试动作,这使得其应用受到一定限制。为支持测试动作,提出一个DLTL扩展DLTL+和一个判定DLTL+公式可满足性的tableau算法,并给出了算法的正确性以及其时间复杂度为2O(n)的证明。分析表明,DLTL+提供了一种直接的、有效的测试动作支持方式,该方式比已知的其他方式更具有实际应用价值。     

基于增量DFT 的相似时序检索算法

首先提出一种在时域上计算时序数据扩展距离的新算法,该算法时间复杂度为O(n×m),能够解决时序数据在Y轴上的漂移和伸缩后仍然保留相似性的问题;然后提出一种在频域上计算时序数据扩展距离和在长时序中搜索相似子序列的新算法,该算法时间复杂度仅为O(n×fc),效率很高,便于在线实现,而且同样能够适应时序数据扩展距离的定义;最后给出时序数据和线性加权时序数据的增量式DFT算法,可以对长时序的各个窗口进行增量式的降维,将传统的O(n×m×fc)工作改进成O(n×fc).     

基于组合逻辑最小化技术的时序逻辑综合方法

介绍一种以组合逻辑最小化工具为基础，提出按满足压缩状态表约束关系进行状态分配的新思想，通过一系列的转换，可完成从描述时序逻辑的原始状态表到满足该状态表状态转换要求的由ＰＬＡ作为组合逻辑部件的时序逻辑电路的转换。由于该时序逻辑综合新方法在处理过程中要涉及解大型覆盖表的问题，为此提出满足压缩状态表约束关系的状态分配的简化算法。文中用一些实例说明简化算法的具体运算过程。结果表明简化算法可导出满足原始状态表的较简化的时序逻辑表达式。     

基于关联选择的可逆逻辑综合算法

可逆逻辑综合是可逆计算的重要内容,为了解决可逆逻辑综合中可逆电路构造和优化问题,提出一种基于关联选择的可逆逻辑综合算法及相应的优化算法.将可逆函数用真值表表示,按真值表从上往下的顺序综合,并若干相关联变量作为综合的目标位,分别计算相对混乱度和绝对混乱度,以最小混乱度原则选取可逆逻辑门.该算法及其优化算法的时间复杂度为O(n2×2n),空间复杂度为O(n×2n),优于最佳算法的空间复杂度O(2n!).通过C++语言实现对3变量全部函数及部分4变量函数的综合,并与其他可逆逻辑综合算法的结果及benchmark范例比较,结果表明平均门数均具有一定优势.     

由一阶逻辑公式得到命题逻辑可满足性问题实例

命题逻辑可满足性(SAT)问题是计算机科学中的一个重要问题.近年来许多学者在这方面进行了大量的研究,提出了不少有效的算法.但是,很多实际问题如果用一组一阶逻辑公式来描述,往往更为自然.当解释的论域是一个固定大小的有限集合时,一阶逻辑公式的可满足性问题可以等价地归约为SAT问题.为了利用现有的高效SAT工具,提出了一种从一阶逻辑公式生成SAT问题实例的算法,并描述了一个自动的转换工具,给出了相应的实验结果.还讨论了通过增加公式来消除同构从而减小搜索空间的一些方法.实验表明,这一算法是有效的,可以用来解决数学研究和实际应用中的许多问题.     

A BDD SAT solver for satisfiability testing: An industrial case study

The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. In this paper, we give a BDD (Binary Decision Diagrams) SAT solver for practical asynchronous circuit design. The BDD SAT solver consists of a structural SAT formula preprocessor and a complete, incremental SAT algorithm that is able to find an optimal solution. The preprocessor compresses a large size SAT formula representing the circuit into a number of smaller SAT formulas. This avoids the problem of solving very large SAT formulas. Each small size SAT formula is solved by the BDD SAT algorithm efficiently. Eventually, the results of these subproblems are integrated together that contribute to the solution of the original problem. According to recent industrial assessments, this BDD SAT solver provides solutions to the practical, industrial asynchronous circuit design problems.This research is supported in part by the 1993 ACM/IEEE Design Automation Award, by the Alberta Microelectronics Graduate Scholarship, by the NSERC research grant OGP0046423, and was supported in part by the NSERC strategic grant MEF0045793.Presently, Jun Gu is on leave with the Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.     

Probability logic and optimization SAT: The PSAT and CPA models

Both probabilistic satisfiability (PSAT) and the check of coherence of probability assessment (CPA) can be considered as probabilistic counterparts of the classical propositional satisfiability problem (SAT). Actually, CPA turns out to be a particular case of PSAT; in this paper, we compare the computational complexity of these two problems for some classes of instances. First, we point out the relations between these probabilistic problems and two well known optimization counterparts of SAT, namely Max SAT and Min SAT. We then prove that Max SAT with unrestricted weights is NP-hard for the class of graph formulas, where Min SAT can be solved in polynomial time. In light of the aforementioned relations, we conclude that PSAT is NP-complete for ideal formulas, where CPA can be solved in linear time.     

Safety property verification using sequential SAT and bounded model checking

Model checkers verify properties of safety- or business-critical systems. The main idea behind model checking is to convert a design's verification into a problem of checking key design properties expressed as a set of temporal logic formulas. The graph representing the design's state space then becomes the basis for testing these formulas' satisfiability (SAT). This divide-and-conquer approach provides an overall test for design correctness. We describe a method for checking safety properties using sequential SAT. SSAT can efficiently prove true properties by harnessing the power of bounded model checking (BMC) using SAT, but without the need for a pre-computed correctness threshold. Using a standard set of benchmarks, we conducted experiments to compare the runtime behavior of SSAT with BMC and binary decision diagrams (BDDs).     

求解SAT问题的线性半定规划算法

将线性半定规划应用到SAT问题的求解过程中。首先将SAT实例转化为整数规划问题,然后松弛为线性规划模型,最后再转化为一般的线性半定规划模型去求解。用SDPA-M软件求解线性半定规划问题后,规定了如何根据目标函数值去判定SAT实例和当CNF公式可满足时如何根据最优指派的概率X^＊i（i=1,…,n）去进行变元赋值,以期求得该公式的可满足指派。上述算法不仅可以判定SAT问题,而且对于符合算法规定可满足的CNF公式皆可给出一个可满足指派。求解SAT问题的线性半定规划算法在文章中被描述并被给予相应算例。     

Answer Set Programming Based on Propositional Satisfiability

Answer set programming (ASP) emerged in the late 1990s as a new logic programming paradigm that has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced. All these reductions, however, are limited to a subclass of logic programs or introduce new variables or may produce exponentially bigger propositional formulas. In this paper, we present a SAT-based procedure, called ASPSAT, that (1) deals with any (nondisjunctive) logic program, (2) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (3) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASPSAT. From a practical perspective, we have (1) implemented ASPSAT in Cmodels, (2) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (3) conducted an extensive comparative analysis involving other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered and that the reasoning strategies that work best on ‘small but hard’ problems are ineffective on ‘big but easy’ problems and vice versa.     

Probability logic and optimization SAT: The PSAT and CPA models

Both probabilistic satisfiability (PSAT) and the check of coherence of probability assessment (CPA) can be considered as probabilistic counterparts of the classical propositional satisfiability problem (SAT). Actually, CPA turns out to be a particular case of PSAT; in this paper, we compare the computational complexity of these two problems for some classes of instances. First, we point out the relations between these probabilistic problems and two well known optimization counterparts of SAT, namely Max SAT and Min SAT. We then prove that Max SAT with unrestricted weights is NP-hard for the class of graph formulas, where Min SAT can be solved in polynomial time. In light of the aforementioned relations, we conclude that PSAT is NP-complete for ideal formulas, where CPA can be solved in linear time.     

Beyond the structure of SAT formulas

Nowadays, many real-world problems are encoded into SAT instances and efficiently solved by modern SAT solvers. These solvers, usually known as Conflict-Driven Clause Learning (CDCL) SAT solvers, include a variety of sophisticated techniques, such as clause learning, lazy data structures, conflict-based adaptive branching heuristics, or random restarts, among others. However, the reasons of their efficiency in solving real-world, or industrial, SAT instances are still unknown. The common wisdom in the SAT community is that these technique exploit some hidden structure of real-world problems.In this thesis, we characterize some important features of the underlying structure of industrial SAT instances. Namely, they are the community structure and the self-similar structure. We observe that most industrial SAT formulas, viewed as graphs, have these two properties. This means that (i) in a graph with a clear community structure, i.e. having high modularity, we can find a partition of its nodes into communities such that most edges connect nodes of the same community; and (ii) in a graph with a self-similar pattern, i.e. being fractal, its shape is kept after re-scalings, i.e., grouping sets of nodes into a single node. We also analyze how these structures are affected by the effects of CDCL techniques during the search.Using the previous structural studies, we propose three applications. First, we face the problem of generating pseudo-industrial random SAT instances using the notion of modularity. Our model generates instances similar to (classical) random SAT formulas when the modularity is low, but when this value is high, our model is also adequate to model realistic pseudo-industrial problems. Second, we propose a method based on the community structure of the instance to detect relevant learnt clauses. Our technique augments the original instance with this set of relevant clauses, and this results into an overall improvement of the efficiency of several state-of-the-art CDCL SAT solvers. Finally, we analyze the classification of industrial SAT instances into families using the previously analyzed structure features, and we compare them to other classifiers commonly used in portfolio SAT approaches.In summary, this dissertation extends the understandings of the structure of SAT instances, with the aim of better explaining the success of CDCL techniques and possibly improve them, and propose a number of applications based on this analysis of the underlying structure of SAT formulas.     

基于SAT工具的限界模型检测归约方法

限界模型检测主要对路径上的属性进行检测,基于此给出一种编码方法,将LTL公式在路径上展开,从而将限界模型检测转换为命题逻辑的可满足性问题,使用SAT求解工具来完成模型检测过程。阐述归约过程的正确性与完全性,通过一个具体例子证明了该方法的有效性。