A critical question about Large Language Models (LLMs) is whether their apparent
deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure …

Neuro-symbolic learning generally consists of two separated worlds, ie, neural network
training and symbolic constraint solving, whose success hinges on symbol grounding, a …

We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC)
algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of …

We give new algorithms based on Markov chains to sample and approximately count
satisfying assignments to k-uniform CNF formulas where each variable appears at most d …

Let Φ be a random k-CNF formula on n variables and m clauses, where each clause is a
disjunction of k literals chosen independently and uniformly. Our goal is, for most Φ, to …

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction
problems (CSPs) in a local lemma regime. Ihe expected running time of our algorithm is …

We give a simple combinatorial algorithm to deterministically approximately count the
number of satisfying assignments of general constraint satisfaction problems (CSPs) …

Let Φ=(V,C) be a constraint satisfaction problem on variables v_1,...,v_n such that each
constraint depends on at most k variables and such that each variable assumes values in an …

We give a Markov chain based perfect sampler for uniform sampling solutions of constraint
satisfaction problems (CSP). Under some mild Lov\'asz local lemma conditions where each …

We study the single-site Glauber dynamics for the fugacity $\lambda $, Hard-core model on
the random graph $ G (n, d/n) $. We show that for the typical instances of the random graph …