Browsing by Author "Chakraborty, Supratik"

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    Algorithmic Improvements in Approximate Counting for Probabilistic Inference: From Linear to Logarithmic SAT Calls*
    (2016-11-28) Chakraborty, Supratik; Meel, Kuldeep S.; Vardi, Moshe Y.
    Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-the-art hashing-based counting algorithms use an NP oracle (SAT solver in practice), such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new approach to hashing-based approximate model counting in which the number of oracle invocations grows logarithmically in n, while still providing strong theoretical guarantees. We use this technique to design an algorithm for #CNF with probably approximately correct (PAC) guarantees. Our experiments show that this algorithm outperforms state-of-the-art techniques for approximate counting by 1-2 orders of magnitude in running time. We also show that our algorithm can be easily adapted to give a new fully polynomial randomized approximation scheme (FPRAS) for #DNF
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    Constrained Counting and Sampling: Bridging the Gap Between Theory and Practice
    (2017-09-29) Meel, Kuldeep Singh; Chakraborty, Supratik; Chaudhuri, Swarat; Duenas-Osorio, Leonardo; Seshia, Sanjit A.; Vardi, Moshe Y.
    Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, privacy, probabilistic reasoning, and constrained-random verification. In constrained counting, the task is to compute the total weight, subject to a given weighting function, of the set of solutions of the given constraints. In constrained sampling, the task is to sample randomly, subject to a given weighting function, from the set of solutions to a set of given constraints. Consequently, Constrained counting and sampling have been subject to intense theoretical and empirical investigations over the years. Prior work, however, offered either heuristic techniques with poor guarantees of accuracy or approaches with proven guarantees but poor performance in practice. In this thesis, we introduce a novel hashing-based algorithmic framework for constrained sampling and counting that combines the classical algorithmic technique of universal hashing with the dramatic progress made in Boolean reasoning solving, in particular, {\SAT} and {\SMT}, over the past two decades. By exploiting the connection between definability of formulas and variance of the distribution of solutions in a cell defined by 3-universal hash functions, we introduced an algorithmic technique, {\MIS}, that reduced the size of XOR constraints employed in the underlying universal hash functions by as much as two orders of magnitude. The resulting frameworks for counting ( {\ScalApproxMC}) and sampling ({\UniGen}) can handle formulas with up to million variables representing a significant boost up from the prior state of the art tools' capability to handle few hundreds of variables. If the initial set of constraints is expressed as Disjunctive Normal Form (DNF), {\ScalApproxMC} is the only known Fully Polynomial Randomized Approximation Scheme (FPRAS) that does not involve Monte Carlo steps. We demonstrate the utility of the above techniques on various real applications including probabilistic inference, design verification and estimating the reliability of critical infrastructure networks during natural disasters. The high parallelizability of our approach opens up new directions for development of artificial intelligence tools that can effectively leverage high-performance computing resources.
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    Sampling Techniques for Boolean Satisfiability
    (2014-04-24) Meel, Kuldeep; Vardi, Moshe Y.; Chakraborty, Supratik; Chaudhuri, Swarat; Nakhleh, Luay K.
    Boolean satisfiability (SAT) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the problems of generating satisfying uniformly at random, and of counting the total number of satisfying assignments have also attracted significant theoretical and practical interest over the years. Prior work offered heuristic approaches with very weak or no guarantee of performance, and theoretical approaches with proven guarantees, but poor performance in practice. We propose a novel approach based on limited-independence hashing that allows us to design algorithms for both problems, with strong theoretical guarantees and scalability extending to thousands of variables. Based on this approach, we present two practical algorithms, UniWit: a near uniform generator and ApproxMC: the first scalable approximate model counter, along with reference implementations. Our algorithms work by issuing polynomial calls to SAT solver. We demonstrate scalability of our algorithms over a large set of benchmarks arising from different application domains.