Related papers: Solving constraint-satisfaction problems with dist…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing,…
To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…
Recently many neural models have been proposed to solve combinatorial puzzles by implicitly learning underlying constraints using their solved instances, such as sudoku or graph coloring (GCP). One drawback of the proposed architectures,…
The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint…
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
Constraint Satisfaction Problems (CSPs) present significant challenges to artificial intelligence due to their intricate constraints and the necessity for precise solutions. Existing symbolic solvers are often slow, and prior research has…
Arkin et al.~\cite{ArkinBCCJKMM17} recently introduced \textit{partitioned pairs} network optimization problems: given a metric-weighted graph on $n$ pairs of nodes, the task is to color one node from each pair red and the other blue, and…
We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
In this paper, we investigate a constrained optimal coordination problem for a class of heterogeneous nonlinear multi-agent systems described by high-order dynamics subject to both unknown nonlinearities and external disturbances. Each…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…
Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We investigate the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that augments existing…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…
We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models…
The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
A variety of behaviors like spatial navigation or bodily motion can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of…