Related papers: Positive 1-in-3-SAT admits a non-trivial Kernel
The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we…
Adversarial SAT (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity…
We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method…
The CTL learning problem consists in finding for a given sample of positive and negative Kripke structures a distinguishing CTL formula that is verified by the former but not by the latter. Further constraints may bound the size and shape…
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the so-called Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts…
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…
Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
This paper introduces SATformer, a novel Transformer-based approach for the Boolean Satisfiability (SAT) problem. Rather than solving the problem directly, SATformer approaches the problem from the opposite direction by focusing on…
We show that, for a positive integer $r$, every minimal 1-saturating set in ${\rm PG}(r-1,2)$ of size at least ${11/36} 2^r+3$ is either a complete cap or can be obtained from a complete cap $S$ by fixing some $s\in S$ and replacing every…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
In this paper we describe the volunteer computing project SAT@home, developed and maintained by us. This project is aimed at solving hard instances of the Boolean satisfiability problem (SAT). We believe that this project can be a useful…
As Cook-Levin theorem showed, every NP problem can be reduced to SAT in polynomial time. In this paper I show a simpler and more efficent method to reduce some factorization problems to the satisfability of a boolean formula.
The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The…