Satisfiability Problem: Theory and Applications最新文献

{"title":"Complexity of hierarchically and 1-dimensional periodically specified problems I: Hardness results","authors":"M. Marathe, H. Hunt, R. Stearns, V. Radhakrishnan","doi":"10.1090/dimacs/035/05","DOIUrl":"https://doi.org/10.1090/dimacs/035/05","url":null,"abstract":"We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"447 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123594522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algorithms for the satisfiability (SAT) problem: A survey","authors":"J. Gu, P. Purdom, J. Franco, B. Wah","doi":"10.1090/dimacs/035/02","DOIUrl":"https://doi.org/10.1090/dimacs/035/02","url":null,"abstract":"Abstract : The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer aided design, computer aided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the satisfiability problems.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122168093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The polynomial time decidability of simulation relations for finite processes: A HORNSAT based approach","authors":"S. Shukla, D. Rosenkrantz, H. Hunt, R. Stearns","doi":"10.1090/dimacs/035/17","DOIUrl":"https://doi.org/10.1090/dimacs/035/17","url":null,"abstract":"We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations for-nite state processes. Our approach involves eecient reductions to the satissability problem for Horn formulas. It applies directly and naturally to most of the simulation preorders and equivalence relations, studied in the literature. Here we illustrate our methodology by deriving eecient algorithms for a number of such relations. For some of these relations, we present polynomial time algorithms for the rst time in the literature. We also present a HORNSAT based interpretation of the existing bottom-up algorithm for bisimulation equivalence KS90] to provide a better understanding of such bottom-up partition based methods KS90, PT87]. Corollaries of our results include an NC algorithm for bisimulation equivalence for deterministic transition system (posed as an open problem in GHR95]), an easy algorithm for computing simulations on nite graphs HHK95] etc. Our approach naturally gives rise to algorithms which are on the y VW86, FM91], local CS91, Lar92] and incremental SS94]. Moreover , diagnostic information CC92, FM91] can be obtained without any additional complexity overhead in this methodology.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127557517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Satisfiability of 3CNF formulas with small clause/variable-ratio","authors":"K. Iwama, Kazuya Takaki","doi":"10.1090/dimacs/035/07","DOIUrl":"https://doi.org/10.1090/dimacs/035/07","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132363022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Backtracking and probing","authors":"P. Purdom, G. Haven","doi":"10.1090/dimacs/035/03","DOIUrl":"https://doi.org/10.1090/dimacs/035/03","url":null,"abstract":"We analyze two algorithms for solving constraint satisfaction problems. One of these algorithms, Probe Order Backtracking, has an average running time much faster than any previously analyzed algorithm for problems where solutions are common. Probe Order Backtracking uses a probing assignment a prese-lected test assignment to unset variables to help guide the search for a solution to a constraint satisfaction problem. If the problem is not satissed when the unset variables are temporarily set to the probing assignment , the algorithm selects one of the relations that the probing assignment fails to satisfy and selects an unset variable from that relation. Then at each b a c ktracking step it generates subproblems by setting the selected variable each p o s s i b l e w ay. It simpliies each subproblem, and tries the same technique on them. For random problems with v variables, t clauses, and probability p that a literal appears in a clause, the average time for Probe Order Backtracking is no more than v n when p lnt=v plus lower order terms. The best previous result was p p ln t=v. When the algorithm is combined with an algorithm of Franco that makes selective use of resolution, the average time for solving random problems is polynomial for all values of p when t On 1=3 v=ln v 2=3. The best previous result was t On 1=3 v=ln v 1=6. Probe Order Backtracking also runs in polynomial average time when p 1=v, compared with the best previous result of p 1=2v. With Probe Order Backtracking the range of p that leads to more than polynomial time is much smaller than that for previously analyzed algorithms. 1 Backtracking The constraint satisfaction problem is to determine whether a set of constraints over discrete variables can be satissed. Each constraint m ust have a form that is easy to evaluate, so any diiculty in solving such a problem comes from the interaction between the constraints and the need to nd a setting for the variables that simultaneously satisses all of the constraints. Constraint satisfaction problems are extremely common. Indeed, the proof that a problem is NP-complete implies an eecient w ay to transform the problem into a constraint satisfaction problem. Most NP-complete problems are initially stated as constraint satisfaction problems. A few special forms of constraint satisfaction problems have known algorithms that solve problem instances in polynomial worst-case time. …","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"67 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134141965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local search for channel assignment in cellular mobile networks","authors":"C. Rushforth, Wei Wang","doi":"10.1090/dimacs/035/22","DOIUrl":"https://doi.org/10.1090/dimacs/035/22","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123936724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A better upper bound for the unsatisfiability threshold","authors":"L. Kirousis, E. Kranakis, D. Krizanc","doi":"10.1090/dimacs/035/18","DOIUrl":"https://doi.org/10.1090/dimacs/035/18","url":null,"abstract":"Let be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number such that if the ratio of the number of clauses over the number of variables of strictly exceeds , then is almost certainly unsatissable. By a well known and more or less straightforward argument, it can be shown that 5:191. This upper bound was improved by Kamath, Motwani, Palem, and Spirakis to 4.758, by rst providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of is around 4.2. In this work, we show that this upper bound can be improved to 4.667. Our proof is elementary and short, and does not use unveriiable mechanical calculations. Moreover it generalizes in a straightforward manner to k-SAT, for k > 3.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129553495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Surrogate constraint analysis-new heuristics and learning schemes for satisfiability problems","authors":"A. Løkketangen, F. Glover","doi":"10.1090/dimacs/035/14","DOIUrl":"https://doi.org/10.1090/dimacs/035/14","url":null,"abstract":"Surrogate constraint analysis has been applied effectively to a variety of combinatorial optimization problems, as a foundation for both exact and heuristic methods. In the heuristic domain, surrogate constraint methods are particularly suited to the creation of associated learning procedures and to the application of probabilistic decisions. We show that these approaches are natural and effective for satisfiability (SAT) problems. Added motivation comes from observing that the current best exact and heuristic procedures for multidimensional knapsack problems are provided independently by surrogate constraint methods and probabilistic methods that use memory and learning structures (derived from tabu search). We show that the SAT problem can be formulated as a special instance of a binary-choice multidimensional knapsack problem (or equivalently, a binary-choice generalized covering problem), and demonstrate how surrogate constraint analysis can be specialized in a particularly convenient way to exploit the structure of this problem. Our approach incorporates simple (first order) instances of adaptive memory structures characteristic of tabu search implementations, to give a learning effect to guide the search. This use of memory adds a dimension to the solution process that has not adequately been examined in the past. We find that the combination of surrogate constraint analysis and simple learning proves more effective than probabilistic search designs, including those that encompass probabilistic rules that have been highly favored in previous SAT approaches. These outcomes motivate a closer look at surrogate strategies and more advanced ways of integrating them with adaptive memory and learning procedures.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122650872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the use of second order derivatives for the satisfiability problem","authors":"H. Maaren","doi":"10.1090/dimacs/035/21","DOIUrl":"https://doi.org/10.1090/dimacs/035/21","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126021731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving MAX-SAT with non-oblivious functions and history-based heuristics","authors":"R. Battiti, M. Protasi","doi":"10.1090/dimacs/035/19","DOIUrl":"https://doi.org/10.1090/dimacs/035/19","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121555644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}