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

Incremental Verification of Timing Constraints for Real-Time Systems

Testing constraints for real-time systems are usually verified through the satisfiability of propositional formulae. In this paper, we propose an alternative where the verification of timing constraints can be done by counting the number of truth assignments instead of boolean satisfiability. This number can also tell us how “far away” is a given specification from satisfying its safety assertion. Furthermore, specifications and safety assertions are often modified in an incremental fashion, where problematic bugs are fixed one at a time. To support this development, we propose an incremental algorithm for counting satisfiability. Our proposed incremental algorithm is optimal as no unnecessary nodes are created during each counting. This works for the class of path RTL. To illustrate this application, we show how incremental satisfiability counting can be applied to a well-known rail-road crossing example, particularly when its specification is still being refined.Singapore-MIT Alliance (SMA