Related papers: The Structure of In-Place Space-Bounded Computatio…
In this paper, due to the important value in practical applications, we consider the coded distributed matrix multiplication problem of computing $AA^\top$ in a distributed computing system with $N$ worker nodes and a master node, where the…
Kolmogorov's representation theorem provides a framework for decomposing any arbitrary real-valued, multivariate, and continuous function into a two-layer nested superposition of a finite number of functions. The functions at these two…
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…
We investigate the space complexity of refuting $3$-CNFs in Resolution and algebraic systems. We prove that every Polynomial Calculus with Resolution refutation of a random $3$-CNF $\phi$ in $n$ variables requires, with high probability,…
Federated learning (FL) is a decentralized machine learning approach where independent learners process data privately. Its goal is to create a robust and accurate model by aggregating and retraining local models over multiple rounds.…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
We show that for all functions $t(n) \geq n$, every multitape Turing machine running in time $t$ can be simulated in space only $O(\sqrt{t \log t})$. This is a substantial improvement over Hopcroft, Paul, and Valiant's simulation of time…
A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…
We give a novel descriptive-complexity theoretic characterization of L and NL computable queries over finite structures using traversal invariance. We summarize this as (N)L = FO + (breadth-first) traversal-invariance.
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
The joint optimization of the integer matrix $\mathbf{A}$ and the power scaling matrix $\mathbf{D}$ is central to achieving the capacity-approaching performance of Integer-Forcing (IF) precoding. This problem, however, is known to be…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
We introduce the entangled quantum polynomial hierarchy $\mathsf{QEPH}$ as the class of problems that are efficiently verifiable given alternating quantum proofs that may be entangled with each other. We prove $\mathsf{QEPH}$ collapses to…
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitrary fields. The evidence for these claims is restricting…
Fast combinational multipliers with large bit widths can occupy significant silicon area, which also drives up power consumption. Area can be reduced through resource sharing (i.e., folding) at the expense of lower throughput, which is…