Satisfiability Problem: Theory and Applications最新文献

{"title":"A GRASP clustering technique for circuit partitioning","authors":"S. Areibi, A. Vannelli","doi":"10.1090/dimacs/035/23","DOIUrl":"https://doi.org/10.1090/dimacs/035/23","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"36 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":"116937396","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":"Approximate solution of weighted MAX-SAT problems using GRASP","authors":"M. G. Resende, L. Pitsoulis, P. Pardalos","doi":"10.1090/dimacs/035/11","DOIUrl":"https://doi.org/10.1090/dimacs/035/11","url":null,"abstract":"Computing the optimal solution to an instance of the weighted maximum satissability problem (MAX-SAT) is diicult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MAX-SAT problems. The heuristic is tested on a large set of test instances. Computational experience indicates the suitability of GRASP for this class of problems.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"42 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":"126290890","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 imbalance of distributions of solutions of CNF-formulas and its impact on satisfiability solvers","authors":"Ewald Speckenmeyer, Max Böhm, Peter Heusch","doi":"10.1090/dimacs/035/20","DOIUrl":"https://doi.org/10.1090/dimacs/035/20","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"149 5 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":"130818510","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":"Relative size of certain polynomial time solvable subclasses of satisfiability","authors":"J. Franco","doi":"10.1090/dimacs/035/04","DOIUrl":"https://doi.org/10.1090/dimacs/035/04","url":null,"abstract":"Abstract : We determine, according to a certain measure, the relative sizes of several well known polynomially solvable subclasses of SAT. The measure we adopt is the probability that randomly selected k-SAT formulas belong to the subclass of formulas in question. This probability is a function of the ratio r of clauses to variables and we determine those ranges of this ratio that result in membership with high probability. We show, for any fixed r > 4/(k(k - 1)), the probability that a random formula is SLUR, q-Horn, extended Horn, CC-balanced, or renamable Horn tends to 0 as n approaches infinity. We also show that most random unsatisfiable formulas are not members of one of these subclasses.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"AES-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":"126553520","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":"Multispace search for satisfiability and NP-hard problems","authors":"J. Gu","doi":"10.1090/dimacs/035/12","DOIUrl":"https://doi.org/10.1090/dimacs/035/12","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"30 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":"116588194","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 branch and cut algorithm for MAX-SAT and weighted MAX-SAT","authors":"S. Joy, J. Mitchell, B. Borchers","doi":"10.1090/dimacs/035/13","DOIUrl":"https://doi.org/10.1090/dimacs/035/13","url":null,"abstract":"DIMACS Series in Discrete Mathematicsand Theoretical Computer ScienceVolume00, 19xxA Branch and Cut Algorithm for MAX-SAT and WeightedMAX-SATSteveJoy, John Mitchell, and Brian BorchersAbstract.We describ e a branch and cut algorithm for b oth MAX-SAT andweighted MAX-SAT. This algorithm uses the GSAT pro cedure as a primalheuristic. At eachnode we solve a linear programming (LP) relaxation of theproblem. Twostyles of separating cuts are added: resolution cuts and o ddcycle inequalities.We compare our algorithm to an extension of the Davis Putnam Love-land (EDPL) algorithm. Our algorithm is more e ective than EDPL on someproblems, notably MAX-2-SAT. EDPL is more e ective on some other classesof problems.1. Intro ductionThe satis ability problem (SAT) is a problem in prop ositional logic. A logicformula consists of the conjunction of clauses. Each clause consists of a disjunctionof literals. Each literal is a variable or its negation. The SAT problem seeks to ndan assignment to the variables which satis es the logic formula, or an indicationthat no such assignment exists. The satis ability problem is NP-complete [5].There are a numb er of exact algorithms for the satis ability problem. Theseinclude Davis-Putnam-Loveland [4,23], resolution [26], and integer programmingapproaches [1,16, 18, 20,21]. A numb er of heuristics that use randomizationalso exist; the rst randomized lo cal search algorithm for satis abilitywas due toGu [9, 10, 11, 12]. Other algorithms include the GSAT heuristic [29, 30] and theGRASP heuristic [25]. For surveys of algorithms for SAT problems see [13,14].In this pap er weinvestigate the related MAX-SAT problem. Given a collectionof clauses, we seek a variable assignment that maximizes the numb er of satis edclauses. The weighted MAX-SAT problem assigns a wt to each clause, and seeksan assignment that maximizes the sum of the weights of the satis ed clauses. Bothof these problems are NP-hard. It is p ossible to approximate MAX-SAT within afactor of 1.325 in p olynomial time [6].Most SAT heuristics have b een extended to MAX-SAT. Several heuristics forMAX-SAT are summarized in Hansen and Jaumard [15]. The GSAT heuristic hasalso b een extended to weighted MAX-SAT[22].1991Mathematics Subject Classi cation.03B05, 49M35, 65K05, 90C10.Research supp orted by ONR Grant N00014{94{1{0391 to Rensselaer Polytechnic Institute.c0000 American Mathematical So ciety1052-1798/00 $1.00 + $.25 p er page1","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"44 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":"132758504","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":"Worst-case analysis, 3-SAT decision and lower bounds: Approaches for improved SAT algorithms","authors":"Oliver Kullman","doi":"10.1090/dimacs/035/06","DOIUrl":"https://doi.org/10.1090/dimacs/035/06","url":null,"abstract":"New methods for worst-case analysis and (3-)SAT decision are presented. The focus lies on the central ideas leading to the improved bound 1:5045 n for 3-SAT decision ((Ku96]; n is the number of variables). The implications for SAT decision in general are discussed and elucidated by a number of hypothesis'. In addition an exponential lower bound for a general class of SAT-algorithms is given and the only possibilities to remain under this bound are pointed out. In this article the central ideas leading to the improved worst-case upper bound 1:5045 n for 3-SAT decision ((Ku96]) are presented. 1) In nine sections the following subjects are treated: 1. Gauging of branchings\": The -function\" and the concept of a distance function\" is introduced, our main tools for the analysis of SAT algorithms, and, as we propose, also a basis for (complete) practical algorithms. 2. Estimating the size of arbitrary trees\": The -Lemma\" is presented, yielding an upper bound for the number of leaves of arbitrary trees, and our central criterion for good\" distance functions is discussed. 3. The basic idea for the improved 3-SAT algorithm\": Starting from the worst-case bounds 1:619 n ((MoSp79], Lu84], MoSp85]) and 1:579 n ((Sch92]), we explain that observation which has been the origin of our investigations. 4. The reened distance function n ? \": The main tool for the (reened) analysis, the improved distance function, is discussed ((n is the loss of variables, while counts the variation in the number of 2-clauses by means 1) For the history of the subject, see Ku96], and also KuLu96]; for the whole eld of SAT algorithms see GPFW96].","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"55 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":"132856100","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":"Branching rules for propositional satisfiability test","authors":"Jinchang Wang","doi":"10.1090/dimacs/035/09","DOIUrl":"https://doi.org/10.1090/dimacs/035/09","url":null,"abstract":"","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"43 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":"131381576","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":"Some fundamental properties of Boolean ring normal forms","authors":"J. Hsiang, G. Huang","doi":"10.1090/dimacs/035/16","DOIUrl":"https://doi.org/10.1090/dimacs/035/16","url":null,"abstract":"Boolean ring is an algebraic structure which uses exclusive ? or instead of the usual or. It yields a unique normal form for every Boolean function. In this paper we present several fundamental properties concerning Boolean rings. We present a simple method for deriving the Boolean ring normal form directly from a truth table. We also describe a notion of normal form of a Boolean function with a don't-care condition, and show an algorithm for generating such a normal form. We then discuss two Boolean ring based theorem proving methods for propositional logic. Finally we give some arguments on why the Boolean ring representation had not been used more extensively, and how it can be used in computing.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"75 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":"124810368","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 general stochastic approach to solving problems with hard and soft constraints","authors":"Henry A. Kautz, B. Selman, YueYen Jiang","doi":"10.1090/dimacs/035/15","DOIUrl":"https://doi.org/10.1090/dimacs/035/15","url":null,"abstract":"Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable | in general, one is interested in a set of preferred\" solutions (for example, solutions that minimize some cost function). Preferences can be encoded by incorporating soft\" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAX-SAT ((nd-ing a model that maximizes the sum of the weights of the satissed clauses that make up a problem instance). We generalize a local-search algorithm for satissability to handle weighted MAX-SAT. To demonstrate the eeec-tiveness of our approach, we present experimental results on encodings of a set of well-studied network Steiner-tree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"55 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":"114778719","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}