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

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

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

Probabilistic Model Counting with Short XORs

The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique solutions. While theoretically sound, the random parity constraints in that construction have the following drawback: each constraint, on average, involves half of all variables. As a result, the branching factor associated with searching for models that also satisfy the parity constraints quickly gets out of hand. In this work we prove that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added. Our work is based on the realization that the essential feature for random systems of parity constraints to be useful in probabilistic model counting is that the geometry of their set of solutions resembles an error-correcting code.Comment: To appear in SAT 1

Circuit Testing Based on Fuzzy Sampling with BDD Bases

Fuzzy testing of integrated circuits is an established technique. Current approaches generate an approximately uniform random sample from a translation of the circuit to Boolean logic. These approaches have serious scalability issues, which become more pressing with the ever-increasing size of circuits. We propose using a base of binary decision diagrams to sample the translations as a soft computing approach. Uniformity is guaranteed by design and scalability is greatly improved. We test our approach against five other state-of-the-art tools and find our tool to outperform all of them, both in terms of performance and scalability

Uniform and scalable sampling of highly configurable systems

Many analyses on confgurable software systems are intractable when confronted with colossal and highly-constrained confguration spaces. These analyses could instead use statistical inference, where a tractable sample accurately predicts results for the entire space. To do so, the laws of statistical inference requires each member of the population to be equally likely to be included in the sample, i.e., the sampling process needs to be “uniform”. SAT-samplers have been developed to generate uniform random samples at a reasonable computational cost. However, there is a lack of experimental validation over colossal spaces to show whether the samplers indeed produce uniform samples or not. This paper (i) proposes a new sampler named BDDSampler, (ii) presents a new statistical test to verify sampler uniformity, and (iii) reports the evaluation of BDDSampler and fve other state-of-the-art samplers: KUS, QuickSampler, Smarch, Spur, and Unigen2. Our experimental results show only BDDSampler satisfes both scalability and uniformity.Universidad Nacional de Educación a Distancia (UNED) OPTIVAC 096-034091 2021V/PUNED/008Ministerio de Ciencia, Innovación y Universidades RTI2018-101204-B-C22 (OPHELIA)Comunidad Autónoma de Madrid ROBOCITY2030-DIH-CM S2018/NMT-4331Agencia Estatal de Investigación TIN2017-90644-RED

Uniform and scalable SAT-sampling for configurable systems

Several relevant analyses on configurable software systems remain intractable because they require examining vast and highly-constrained configuration spaces. Those analyses could be addressed through statistical inference, i.e., working with a much more tractable sample that later supports generalizing the results obtained to the entire configuration space. To make this possible, the laws of statistical inference impose an indispensable requirement: each member of the population must be equally likely to be included in the sample, i.e., the sampling process needs to be "uniform". Various SAT-samplers have been developed for generating uniform random samples at a reasonable computational cost. Unfortunately, there is a lack of experimental validation over large configuration models to show whether the samplers indeed produce genuine uniform samples or not. This paper (i) presents a new statistical test to verify to what extent samplers accomplish uniformity and (ii) reports the evaluation of four state-of-the-art samplers: Spur, QuickSampler, Unigen2, and Smarch. According to our experimental results, only Spur satisfies both scalability and uniformity.Ministerio de Ciencia, Innovación y Universidades VITAL-3D DPI2016-77677-PMinisterio de Ciencia, Innovación y Universidades OPHELIA RTI2018-101204-B-C22Comunidad Autónoma de Madrid CAM RoboCity2030 S2013/MIT-2748Agencia Estatal de Investigación TIN2017-90644-RED