Papers by Knot Pipatsrisawat
Clone: Solving weighted max-sat in a reduced search space
The maximum satisfiability problem (Max-SAT) is one of the optimization coun-terparts of the Bool... more The maximum satisfiability problem (Max-SAT) is one of the optimization coun-terparts of the Boolean satisfiability problem (SAT). In Max-SAT, given a Boolean formula in conjunctive normal form (CNF), we want to determine the maximum number of clauses that can be satisfied ...
Journal on Satisfiability, Boolean Modeling and Computation - JSAT, 2008
We analyze, in this work, the performance of a recently introduced weighted Max-SAT solver, Clone... more We analyze, in this work, the performance of a recently introduced weighted Max-SAT solver, Clone, in the Max-SAT evaluation 2007. Clone utilizes a novel bound computation based on formula compilation that allows it to search in a reduced search space. We study how additional techniques from the SAT and Max-SAT literature affect the performance of Clone on problems from the evaluation. We then perform further investigations on factors that may affect the performance of leading Max-SAT solvers. We empirically identify two properties of weighted Max-SAT problems that can be used to adjust the difficulty level of the problems with respect to the considered solvers.
We introduce in this paper two new, complete propositional languages and study their properties i... more We introduce in this paper two new, complete propositional languages and study their properties in terms of (1) their support for polytime operations and (2) their ability to represent boolean functions compactly. The new languages are based on a structured version of decomposability-a property that underlies a number of tractable languages. The key characteristic of structured decomposability is its support for a polytime conjoin operation, which is known to be intractable for unstructured decomposability. We show that any CNF can be compiled into formulas in the new languages, whose size is only exponential in the treewidth of the CNF. Our study also reveals that one of the languages we identify is as powerful as OBDDs in terms of answering key inference queries, yet is more succinct than OBDDs.
We present a new algorithm for computing upper bounds for an optimization version of the E-MAJSAT... more We present a new algorithm for computing upper bounds for an optimization version of the E-MAJSAT problem called functional E-MAJSAT. The algorithm utilizes the compilation language d-DNNF which underlies several state-of-the-art algorithms for solving related problems. This bound computation can be used in a branch-and-bound solver for solving functional E-MAJSAT. We then present a technique for pruning values from the branch-and-bound search tree based on the information available after each bound computation. We evaluated the proposed techniques in a MAP solver and a probabilistic conformant planner. In both cases, our experiments showed that the new techniques improved the efficiency of state-of-the-art solvers by orders of magnitude.
Journal of Automated Reasoning, 2010
In this paper, we present a perspective on modern clause-learning SAT solvers that highlights the... more In this paper, we present a perspective on modern clause-learning SAT solvers that highlights the roles of, and the interactions between, decision making and clause learning in these solvers. We discuss two limitations of these solvers from this perspective and discuss techniques for dealing with them. We show empirically that the proposed techniques significantly improve state-of-the-art solvers.
A formal notion of a Boolean-function decomposition was introduced recently and used to provide l... more A formal notion of a Boolean-function decomposition was introduced recently and used to provide lower bounds on various representations of Boolean functions, which are subsets of decomposable negation normal form (DNNF). This notion has introduced a fundamental optimization problem for DNNF representations, which calls for computing decompositions of minimal size for a given partition of the function variables. We consider the problem of computing optimal decompositions in this paper for general Boolean functions and those represented using CNFs. We introduce the notion of an interaction function, which characterizes the relationship between two sets of variables and can form the basis of obtaining such decompositions. We contrast the use of these functions to the current practice of computing decompositions, which is based on heuristic methods that can be viewed as using approximations of interaction functions. We show that current methods can lead to decompositions that are exponentially larger than optimal decompositions, pinpoint the specific reasons for this lack of optimality, and finally present empirical results that illustrate some characteristics of interaction functions in contrast to their approximations.
Bioinformatics/computer Applications in The Biosciences, 2010
Haplotype inference is an important step for many types of analyses of genetic variation in the h... more Haplotype inference is an important step for many types of analyses of genetic variation in the human genome. Traditional approaches for obtaining haplotypes involve collecting genotype information from a population of individuals and then applying a haplotype inference algorithm. The development of high-throughput sequencing technologies allows for an alternative strategy to obtain haplotypes by combining sequence fragments. The problem of 'haplotype assembly' is the problem of assembling the two haplotypes for a chromosome given the collection of such fragments, or reads, and their locations in the haplotypes, which are pre-determined by mapping the reads to a reference genome. Errors in reads significantly increase the difficulty of the problem and it has been shown that the problem is NP-hard even for reads of length 2. Existing greedy and stochastic algorithms are not guaranteed to find the optimal solutions for the haplotype assembly problem. Results: In this article, we proposed a dynamic programming algorithm that is able to assemble the haplotypes optimally with time complexity O(m×2 k ×n), where m is the number of reads, k is the length of the longest read and n is the total number of SNPs in the haplotypes. We also reduce the haplotype assembly problem into the maximum satisfiability problem that can often be solved optimally even when k is large. Taking advantage of the efficiency of our algorithm, we perform simulation experiments demonstrating that the assembly of haplotypes using reads of length typical of the current sequencing technologies is not practical. However, we demonstrate that the combination of this approach and the traditional haplotype phasing approaches allow us to practically construct haplotypes containing both common and rare variants. Contact:
Artificial Intelligence, 2011
In this work, we improve on existing results on the relationship between proof systems obtained f... more In this work, we improve on existing results on the relationship between proof systems obtained from conflict-driven clause-learning SAT solvers and general resolution. Previous contributions such as those by demonstrated that variations on conflict-driven clause-learning SAT solvers corresponded to proof systems as powerful as general resolution. However, the models used in these studies required either an extra degree of non-determinism or a preprocessing step that is not utilized by state-ofthe-art SAT solvers in practice. In this paper, we prove that conflict-driven clauselearning SAT solvers yield proof systems that indeed p-simulate general resolution without the need for any additional techniques. Moreover, we show that our result can be generalized to certain other practical variations of the solvers, which are based on different learning schemes and restart policies. $ This work extends our previous work in with generalized results (Section 6) and additional discussion about related work (Section 7).
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Papers by Knot Pipatsrisawat