UnitWalk: A new SAT solver that uses local search guided by unit clause elimination

In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([27,28] and [30,31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) and unit clause elimination (which is rarely used in local search algorithms). In this paper we do not prove any theoretical bounds. However, we present encouraging results of computational experiments comparing several implementations of our algorithm with other SAT solvers. We also prove that our algorithm is probabilistically approximately complete (PAC).     

UnitWalk: A new SAT solver that uses local search guided by unit clause elimination

In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([27,28] and [30,31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) and unit clause elimination (which is rarely used in local search algorithms). In this paper we do not prove any theoretical bounds. However, we present encouraging results of computational experiments comparing several implementations of our algorithm with other SAT solvers. We also prove that our algorithm is probabilistically approximately complete (PAC).     

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…     

Evaluating Optimized Decision Procedures for Propositional Modal K (m) Satisfiability

Heavily optimized decision procedures for propositional modal satisfiability are now becoming available. Two systems incorporating such procedures for modal K, DLP and KSATC, are tested on randomly generated CNF formulae with several sets of parameters, varying the maximum modal depth and ratio of propositional variable to modal subformulae. The results show some easy-hard-easy behavior, but there is as yet no sharp peak as in propositional satisfiability.     

基于图分解的(3,4)-CNF公式的可满足性

对于规则的(3,4)-CNF公式F,公式F对应的因子图GF恰好是一个(3,4)-双向正则二部图.利用正则二部图的有关性质,证明了对于任意的(3,4)-CNF公式F,若其对应的因子图GF能够被划分为两个(3,2)-双向正则二部图,则F是可满足的.     

Ordered Boolean List (OBL): reducing the footprint for evaluating Boolean expressions

An Expanded Boolean Expression (EBE) does not contain any XOR or EQUAL operators. The occurrence of each variable is a different literal. We provide a linear time algorithm that converts an EBE of n literals into a logically equivalent Ordered Boolean List (OBL) and show how to use the OBL to evaluate the EBE in n steps and O(log log n) space, if the values of the literals are each read once in the order prescribed by the OBL. (An evaluation workspace of 5 bits suffices for all EBEs of up to six billion literals.) The primary application is the SIMD architecture, where the same EBE is evaluated in parallel for different input vectors when rendering solid models on the GPU directly from their Constructive Solid Geometry (CSG) representation. We compare OBL to the Reduced Ordered Binary Decision Diagram (ROBDD) and suggest possible applications of OBL to logic verification and to circuit design.     

O(m~2)时间求解SAT问题的随机算法

传统的求解 SAT问题的随机算法主要是对满足解进行搜索 ,在找不到满足解的情况下 ,则无法正确判断问题的可满足性 .该文提出了两个时间复杂度为 O( m2 )求解 SAT问题的随机算法 Sat Test1和 Sat Test2 ,这里 m为CNF公式中的子句数 .这两个随机算法是通过对不满足解数的估计来判断 SAT问题的可满足性 ,不同于传统的随机算法 .其中第二个算法 Sat Test2在搜索满足解的同时又可以对不满足解数进行估计 ,是对传统随机算法的重要改进 .试验结果表明 ,文中提出的算法对相变区域的难 SAT实例有较好的求解能力 .     

On affine (non)equivalence of Boolean functions

In this paper we construct a multiset S(f) of a Boolean function f consisting of the weights of the second derivatives of the function f with respect to all distinct two-dimensional subspaces of the domain. We refer to S(f) as the second derivative spectrum of f. The frequency distribution of the weights of these second derivatives is referred to as the weight distribution of the second derivative spectrum. It is demonstrated in this paper that this weight distribution can be used to distinguish affine nonequivalent Boolean functions. Given a Boolean function f on n variables we present an efficient algorithm having O(n2²ⁿ ) time complexity to compute S(f). Using this weight distribution we show that all the 6-variable affine nonequivalent bents can be distinguished. We study the subclass of partial-spreads type bent functions known as PS _ap type bents. Six different weight distributions are obtained from the set of PS _ap bents on 8-variables. Using the second derivative spectrum we show that there exist 6 and 8 variable bent functions which are not affine equivalent to rotation symmetric bent functions. Lastly we prove that no non-quadratic Kasami bent function is affine equivalent to Maiorana–MacFarland type bent functions.     

Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)

The Satisfiability Modulo Theories Competition (SMT-COMP) is intended to spark further advances in the decision procedures field, especially for applications in hardware and software verification. Public competitions are a well-known means of stimulating advancement in automated reasoning. Evaluation of SMT solvers entered in SMT-COMP took place while CAV 2005 was meeting. Twelve solvers were entered; 1,352 benchmarks were collected in seven different divisions.     

随机正则(k,r)-SAT问题的可满足临界

研究k-SAT问题实例中每个变元恰好出现r=2s次,且每个变元对应的正、负文字都出现s次的严格随机正则（k,r）-SAT问题.通过构造一个特殊的独立随机实验,结合一阶矩方法,给出了严格随机正则（k,r）-SAT问题可满足临界值的上界.由于严格正则情形与正则情形的可满足临界值近似相等,因此得到了随机正则（k,r）-SAT问题可满足临界值的新上界.该上界不仅小于当前已有的随机正则（k,r）-SAT问题的可满足临界值上界,而且还小于一般的随机k-SAT问题的可满足临界值.因此,这也从理论上解释了在相变点处的随机正则（k,r）-SAT问题实例通常比在相应相变点处同规模的随机k-SAT问题实例更难满足的原因.最后,数值分析结果验证了所给上界的正确性.     

O（m^2）时间求解SAT问题的随机算法

传统的求解SAT问题的随机算法主要是对满足解进行搜索,在找不到满足解的情况下,则无法正确判断问题的可满足性。该文提出了两个时间复杂度为O（m^2）求解SAT问题的随机算法SatTestl和SatTest2,这里m为CNF公式中的子句数。这两个随机算法是通过对不满足解数的估计来判断SAT问题的可满足性,不同于传统的随机算法。其中第二个算法SatTest2在搜索满足解的同时又可以对不满足解数进行估计,是对传统随机算法的重要改进。试验结果表明,文中提出的算法对相变区域的难SAT实例有较好的求解能力。     

(2,1)-Method for solving stiff nonautonomous problems

An L-stable (2,1)-method with second-order accuracy is developed for solving stiff nonautonomous problems. At each step, the right-hand side of the system, as well as Jacobian matrix decomposition are evaluated only once. Efficiency of the integration method is illustrated using ring modulator calculation as an example.     

FDSR:一种面向SD-MANET的快速转发规则下发方法

针对软件定义网络在移动自组织网络里部署传输路径时,需要控制器为路径上所有的节点下发相关流表项,从而造成传输开始需等待较长时间的问题,文中基于分段路由提出了一种快速下发数据转发规则的方法FDSR.控制器会以分段路由的方式,通过在数据包上添加转发路径对应标签的方式下发数据转发规则,并在处理最大堆栈深度问题时,利用标签粘连技...     

Matrix algorithms for solving (in)homogeneous bound state equations

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems.     

Dependent Type System with Subtyping (I)Type Level Transitivity Elimination

Dependent type systems are the basis of many proof development environments.In Aspinall and Compagnoni‘s paper,a system λP≤is proposed as a subtyping extension of the first order dependent type system λP（also called λП）.λP≤has nice meta-theoretic properties including subject reduction and decidability.In this article,we give a reformulation of λP≤，called λП≤.The advantages of λП≤include:type level transitivity elimination propery and pretype-based subtyping system.These features considerably facilitate the meta-theoretical study and further extensions of this system.     

Security Attack Testing (SAT)—testing the security of information systems at design time

For the last few years a considerable number of efforts have been devoted into integrating security issues into information systems development practices. This has led to a number of languages, methods, methodologies and techniques for considering security issues during the developmental stages of an information system. However, these approaches mainly focus on security requirements elicitation, analysis and design issues and neglect testing. This paper presents the Security Attack Testing (SAT) approach, a novel scenario-based approach that tests the security of an information system at the design time. The approach is illustrated with the aid of a real-life case study involving the development of a health and social care information system.     

Automated resolution of connector architectures using constraint solving (ARCAS method)

In current software systems, connectors play an important role by encapsulating the communication and coordination logic. Since they share common patterns (elements) depending on characteristics of the connections, the elements can be predefined and reused. A method of connector implementation based on a composition of predefined elements naturally comprises two steps: resolution of the connector architecture, and creation of the actual connector code based on the architecture. However, manual resolution of a connector architecture is very difficult due to the number of factors to be considered. Thus, the challenge is to come up with an automated method, able to address all the important factors. In this paper, we present a method for automated resolution of connector architectures based on constraint solving techniques. We exploit a propositional logic with relational calculus for defining a connector theory, a constraint specification reflecting both the predefined parts and the important resolution factors, and employ a constraint solver to find a suitable connector architecture as a model of the theory. As a proof of the concept, we show how the theory can be captured in the Alloy language and resolved via the Alloy Analyzer.     

取定s的严格d-正则随机(3,2s)-SAT问题的可满足临界

3-CNF公式的随机难解实例生成对于揭示3-SAT问题的难解实质和设计满足性测试的有效算法有着重要意义.对于整数k>2和s>0,如果在一个k-CNF公式中每个变量正负出现次数均为s,则称该公式是严格正则（k,2s）-CNF公式.受严格正则（k,2s）-CNF公式的结构特征启发,提出每个变量正负出现次数之差的绝对值均为d的严格d-正则（k,2s）-CNF公式,并使用新提出的SDRRK2S模型生成严格d-正则随机（k,2s）-CNF公式.取定整数5<s<11,模拟实验显示,严格d-正则随机（3,2s）-SAT问题存在SAT-UNSAT相变现象和HARD-EASY相变现象.因此,立足于3-CNF公式的随机难解实例生成,研究了严格d-正则随机（3,2s）-SAT问题在s取定时的可满足临界.通过构造一个特殊随机实验和使用一阶矩方法,得到了严格d-正则随机（3,2s）-SAT问题在s取定时可满足临界值的一个下界.模拟实验结果验证了理论证明所得下界的正确性.