11 research outputs found
Bit-Vector Model Counting using Statistical Estimation
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT)
has many applications such as probabilistic inference and quantitative
information-flow security, but it is computationally difficult. Adding random
parity constraints (XOR streamlining) and then checking satisfiability is an
effective approximation technique, but it requires a prior hypothesis about the
model count to produce useful results. We propose an approach inspired by
statistical estimation to continually refine a probabilistic estimate of the
model count for a formula, so that each XOR-streamlined query yields as much
information as possible. We implement this approach, with an approximate
probability model, as a wrapper around an off-the-shelf SMT solver or SAT
solver. Experimental results show that the implementation is faster than the
most similar previous approaches which used simpler refinement strategies. The
technique also lets us model count formulas over floating-point constraints,
which we demonstrate with an application to a vulnerability in differential
privacy mechanisms
Phase Transition Behavior of Cardinality and XOR Constraints
The runtime performance of modern SAT solvers is deeply connected to the
phase transition behavior of CNF formulas. While CNF solving has witnessed
significant runtime improvement over the past two decades, the same does not
hold for several other classes such as the conjunction of cardinality and XOR
constraints, denoted as CARD-XOR formulas. The problem of determining the
satisfiability of CARD-XOR formulas is a fundamental problem with a wide
variety of applications ranging from discrete integration in the field of
artificial intelligence to maximum likelihood decoding in coding theory. The
runtime behavior of random CARD-XOR formulas is unexplored in prior work. In
this paper, we present the first rigorous empirical study to characterize the
runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a
surprising phase-transition that follows a non-linear tradeoff between CARD and
XOR constraints
On Continuous Local BDD-Based Search for Hybrid SAT Solving
We explore the potential of continuous local search (CLS) in SAT solving by
proposing a novel approach for finding a solution of a hybrid system of Boolean
constraints. The algorithm is based on CLS combined with belief propagation on
binary decision diagrams (BDDs). Our framework accepts all Boolean constraints
that admit compact BDDs, including symmetric Boolean constraints and
small-coefficient pseudo-Boolean constraints as interesting families. We
propose a novel algorithm for efficiently computing the gradient needed by CLS.
We study the capabilities and limitations of our versatile CLS solver, GradSAT,
by applying it on many benchmark instances. The experimental results indicate
that GradSAT can be a useful addition to the portfolio of existing SAT and
MaxSAT solvers for solving Boolean satisfiability and optimization problems.Comment: AAAI 2
Phase Transition Behavior of Cardinality and XOR Constraints
The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for several other classes such as the conjunction of cardinality and XOR constraints, denoted as CARD-XOR formulas. The problem of determining satisfiability of CARDXOR formulas is a fundamental problem with wide variety of applications ranging from discrete integration in the field of artificial intelligence to maximum likelihood decoding in coding theory. The runtime behavior of random CARD-XOR formulas is unexplored in prior work. In this paper, we present the first rigorous empirical study to characterize the runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a non-linear tradeoff between CARD and XOR constraints
FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints
The Boolean SATisfiability problem (SAT) is of central importance in computer
science. Although SAT is known to be NP-complete, progress on the engineering
side, especially that of Conflict-Driven Clause Learning (CDCL) and Local
Search SAT solvers, has been remarkable. Yet, while SAT solvers aimed at
solving industrial-scale benchmarks in Conjunctive Normal Form (CNF) have
become quite mature, SAT solvers that are effective on other types of
constraints, e.g., cardinality constraints and XORs, are less well studied; a
general approach to handling non-CNF constraints is still lacking. In addition,
previous work indicated that for specific classes of benchmarks, the running
time of extant SAT solvers depends heavily on properties of the formula and
details of encoding, instead of the scale of the benchmarks, which adds
uncertainty to expectations of running time.
To address the issues above, we design FourierSAT, an incomplete SAT solver
based on Fourier analysis of Boolean functions, a technique to represent
Boolean functions by multilinear polynomials. By such a reduction to continuous
optimization, we propose an algebraic framework for solving systems consisting
of different types of constraints. The idea is to leverage gradient information
to guide the search process in the direction of local improvements. Empirical
results demonstrate that FourierSAT is more robust than other solvers on
certain classes of benchmarks.Comment: The paper was accepted by Thirty-Fourth AAAI Conference on Artificial
Intelligence (AAAI 2020). V2 (Feb 24): Typos correcte