Related papers: Fast counting with tensor networks
In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…
This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to…
Constraint Satisfaction Problems (CSPs, for short) make up a class of problems with applications in many areas of computer science. The first classification of these problems was given by Schaeffer who showed that every CSP over the domain…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…
In this Part II, we apply the general theory developed in Part I to a detailed analysis of the Constraint Satisfaction Problem (CSP). We show how specific types of resolution rules can be defined. In particular, we introduce the general…
The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification that satisfies the constraints in the specification. The problem is NP-hard in general, but…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
We study the Sherali-Adams linear programming hierarchy in the context of promise constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy accepts an instance in terms of a homomorphism problem for an…
We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. An instance of the problem Max (r,2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…
Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…
In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different…
The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…
The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational…
In this paper, we explore the automation of services' compositions. We focus on the service selection problem. In the formulation that we consider, the problem's inputs are constituted by a behavioral composition whose abstract services…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…