Related papers: Biased random k-SAT
We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…
Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We…
To study the structure of solutions for random k-SAT and random CSPs, this paper introduces the concept of average similarity degree to characterize how solutions are similar to each other. It is proved that under certain conditions, as r…
The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiability algorithms, and average-case hardness over this…
We consider Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…
The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…
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…
We present a deterministic approximation algorithm to compute logarithm of the number of `good' truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by `good' we mean that violate a small fraction of clauses).…
We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the…
We study random instances of the weighted $d$-CNF satisfiability problem (WEIGHTED $d$-SAT), a generic W[1]-complete problem. A random instance of the problem consists of a fixed parameter $k$ and a random $d$-CNF formula $\weicnf{n}{p}{k,…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…
Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear…
We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based…
We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\mathbb{F}_2$ over $n$ variables, each equation containing $k \geq 3$ variables, and also consider a "constrained"…
The satisfiability problem is known to be $\mathbf{NP}$-complete in general and for many restricted cases. One way to restrict instances of $k$-SAT is to limit the number of times a variable can be occurred. It was shown that for an…