Related papers: Horn Maximum Satisfiability: Reductions, Algorithm…
The vehicle routing problem is a well known class of NP-hard combinatorial optimisation problems in literature. Traditional solution methods involve either carefully designed heuristics, or time-consuming metaheuristics. Recent work in…
Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem…
Machine learning has become omnipresent with applications in various safety-critical domains such as medical, law, and transportation. In these domains, high-stake decisions provided by machine learning necessitate researchers to design…
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability…
We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
Given a boolean formula $\Phi$(X, Y, Z), the Max\#SAT problem asks for finding a partial model on the set of variables X, maximizing its number of projected models over the set of variables Y. We investigate a strict generalization of…
We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
The monadic shallow linear (MSL) class is a decidable fragment of first-order Horn clauses that was discovered and rediscovered around the turn of the century, with applications in static analysis and verification. We propose a new class of…
We introduce a diversified top-k partial MaxSAT problem, a combination of partial MaxSAT problem and enumeration problem. Given a partial MaxSAT formula F and a positive integer k, the diversified top-k partial MaxSAT is to find k maximal…
Software engineers must make decisions that trade off competing goals (faster vs. cheaper, secure vs. usable, accurate vs. interpretable, etc.). Despite MSR's proven techniques for exploring such goals, researchers still struggle with these…
The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We study the Active Simple Hypothesis Testing (ASHT) problem, a simpler variant of the Fixed Budget Best Arm Identification problem. In this work, we provide novel game theoretic formulation of the upper bounds of the ASHT problem. This…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…