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Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Large Language Models (LLMs) excel at understanding natural language but struggle with optimisation tasks involving multiple constraints and user-defined preferences, which commonly arise in domains such as robotics. We propose a hybrid…
The reactive synthesis problem is to compute a system satisfying a given specification in temporal logic. Bounded synthesis is the approach to bound the maximum size of the system that we accept as a solution to the reactive synthesis…
Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as…
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a…
Machine learning (ML) techniques have been proposed to automatically select the best solver from a portfolio of solvers, based on predicted performance. These techniques have been applied to various problems, such as Boolean Satisfiability,…
Constraint modelling languages such as Essence offer a means to describe combinatorial problems at a high-level, i.e., without committing to detailed modelling decisions for a particular solver or solving paradigm. Given a problem…
Constraint-based learning reduces the burden of collecting labels by having users specify general properties of structured outputs, such as constraints imposed by physical laws. We propose a novel framework for simultaneously learning these…
The Pseudo-Boolean problem deals with linear or polynomial constraints with integer coefficients over Boolean variables. The objective lies in optimizing a linear objective function, or finding a feasible solution, or finding a solution…
We present DeepSAT, a novel end-to-end learning framework for the Boolean satisfiability (SAT) problem. Unlike existing solutions trained on random SAT instances with relatively weak supervision, we propose applying the knowledge of the…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
From CNNs to attention mechanisms, encoding inductive biases into neural networks has been a fruitful source of improvement in machine learning. Adding auxiliary losses to the main objective function is a general way of encoding biases that…
We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability. Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve…
Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and…
We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This…
Streamliner constraints reduce the search space of combinatorial problems by ruling out portions of the solution space. We adapt the StreamLLM approach, which uses Large Language Models (LLMs) to generate streamliners for Constraint…
Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major…
Current pseudo-Boolean solvers implement different variants of the cutting planes proof system to infer new constraints during conflict analysis. One of these variants is generalized resolution, which allows to infer strong constraints, but…
Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of…