Related papers: Tensor Network Contractions for #SAT
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the…
We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…
We present a constructive SAT-based algorithm to determine the multiplicative complexity of a Boolean function, i.e., the smallest number of AND gates in any logic network that consists of 2-input AND gates, 2-input XOR gates, and…
By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
Modern reasoning models, such as OpenAI's o1 and DeepSeek-R1, exhibit impressive problem-solving capabilities but suffer from critical inefficiencies: high inference latency, excessive computational resource consumption, and a tendency…
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…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
Max#SAT is an important problem with multiple applications in security and program synthesis that is proven hard to solve. It is defined as: given a parameterized quantifier-free propositional formula compute parameters such that the number…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to…
The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed…
In this paper we describe the volunteer computing project SAT@home, developed and maintained by us. This project is aimed at solving hard instances of the Boolean satisfiability problem (SAT). We believe that this project can be a useful…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…