Related papers: Second Moment Method on k-SAT: a General Framework

Current algorithms for bounded model checking use SAT methods for checking satisfiability of Boolean formulae. These methods suffer from the potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulae…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…

Phase transition is an important feature of SAT problem. For random k-SAT model, it is proved that as r (ratio of clauses to variables) increases, the structure of solutions will undergo a sudden change like satisfiability phase transition…

Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are…

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…

Since the early 2000s physicists have developed an ingenious but non-rigorous formalism called the cavity method to put forward precise conjectures on phase transitions in random problems [Mezard, Parisi, Zecchina: Science 2002]. The cavity…

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…

Beam search is universally used in full-sentence translation but its application to simultaneous translation remains non-trivial, where output words are committed on the fly. In particular, the recently proposed wait-k policy (Ma et al.,…

Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…

The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…

This is a sequel to our previous articles \cite{Kw23, Kw23a+}. In this work, we apply recent techniques that fall under the banner of `Period Reciprocity' to study moments of $GL(3)\times GL(2)$ $L$-functions in the non-archimedean aspects,…

This paper considers inference in a partially identified moment (in)equality model with many moment inequalities. We propose a novel two-step inference procedure that combines the methods proposed by Chernozhukov, Chetverikov and Kato…

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…

Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…

This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…

We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the…

We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes. Firstly, we reduce the problem of modal refinement over both classes to a…

Statistical inference based on moment conditions and estimating equations is of substantial interest when it is difficult to specify a full probabilistic model. We propose a Bayesian flavored model selection framework based on…

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In…