1,794 research outputs found
Distribution-Aware Sampling and Weighted Model Counting for SAT
Given a CNF formula and a weight for each assignment of values to variables,
two natural problems are weighted model counting and distribution-aware
sampling of satisfying assignments. Both problems have a wide variety of
important applications. Due to the inherent complexity of the exact versions of
the problems, interest has focused on solving them approximately. Prior work in
this area scaled only to small problems in practice, or failed to provide
strong theoretical guarantees, or employed a computationally-expensive maximum
a posteriori probability (MAP) oracle that assumes prior knowledge of a
factored representation of the weight distribution. We present a novel approach
that works with a black-box oracle for weights of assignments and requires only
an {\NP}-oracle (in practice, a SAT-solver) to solve both the counting and
sampling problems. Our approach works under mild assumptions on the
distribution of weights of satisfying assignments, provides strong theoretical
guarantees, and scales to problems involving several thousand variables. We
also show that the assumptions can be significantly relaxed while improving
computational efficiency if a factored representation of the weights is known.Comment: This is a full version of AAAI 2014 pape
Balancing Scalability and Uniformity in SAT Witness Generator
Constrained-random simulation is the predominant approach used in the
industry for functional verification of complex digital designs. The
effectiveness of this approach depends on two key factors: the quality of
constraints used to generate test vectors, and the randomness of solutions
generated from a given set of constraints. In this paper, we focus on the
second problem, and present an algorithm that significantly improves the
state-of-the-art of (almost-)uniform generation of solutions of large Boolean
constraints. Our algorithm provides strong theoretical guarantees on the
uniformity of generated solutions and scales to problems involving hundreds of
thousands of variables.Comment: This is a full version of DAC 2014 pape
Structure Selection from Streaming Relational Data
Statistical relational learning techniques have been successfully applied in
a wide range of relational domains. In most of these applications, the human
designers capitalized on their background knowledge by following a
trial-and-error trajectory, where relational features are manually defined by a
human engineer, parameters are learned for those features on the training data,
the resulting model is validated, and the cycle repeats as the engineer adjusts
the set of features. This paper seeks to streamline application development in
large relational domains by introducing a light-weight approach that
efficiently evaluates relational features on pieces of the relational graph
that are streamed to it one at a time. We evaluate our approach on two social
media tasks and demonstrate that it leads to more accurate models that are
learned faster
Sampling Techniques for Boolean Satisfiability
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, {\UniformWitness}: 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.Comment: MS Thesis submitted to Rice Universit
Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guarantees
Satisfiability Modulo Counting (SMC) encompasses problems that require both
symbolic decision-making and statistical reasoning. Its general formulation
captures many real-world problems at the intersection of symbolic and
statistical Artificial Intelligence. SMC searches for policy interventions to
control probabilistic outcomes. Solving SMC is challenging because of its
highly intractable nature(-complete), incorporating
statistical inference and symbolic reasoning. Previous research on SMC solving
lacks provable guarantees and/or suffers from sub-optimal empirical
performance, especially when combinatorial constraints are present. We propose
XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly
intractable SMC problems with constant approximation guarantees. XOR-SMC
transforms the highly intractable SMC into satisfiability problems, by
replacing the model counting in SMC with SAT formulae subject to randomized XOR
constraints. Experiments on solving important SMC problems in AI for social
good demonstrate that XOR-SMC finds solutions close to the true optimum,
outperforming several baselines which struggle to find good approximations for
the intractable model counting in SMC
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