Related papers: Sampling Techniques for Boolean Satisfiability
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with…
Local search algorithms are well-known methods for solving large, hard instances of the satisfiability problem (SAT). The performance of these algorithms crucially depends on heuristics for setting noise parameters and scoring variables.…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying…
In various areas of computer science, the problem of dealing with a set of constraints arises. If the set of constraints is unsatisfiable, one may ask for a minimal description of the reason for this unsatisifi- ability. Minimal…
This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…
Given a set of items $\mathcal{F}$ and a weight function $\mathtt{wt}: \mathcal{F} \mapsto (0,1)$, the problem of sampling seeks to sample an item proportional to its weight. Sampling is a fundamental problem in machine learning. The…
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…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
Given a Boolean formula $\phi$ over $n$ variables, the problem of model counting is to compute the number of solutions of $\phi$. Model counting is a fundamental problem in computer science with wide-ranging applications. Owing to the…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…
With the increasing adoption of vision-language models (VLMs) in critical decision-making systems such as healthcare or autonomous driving, the calibration of their uncertainty estimates becomes paramount. Yet, this dimension has been…
A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common…
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…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…