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We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of…
In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by…
We present a discrete-time algorithm for nonuniform sampling rate conversion that presents low computational complexity and memory requirements. It generalizes arbitrary sampling rate conversion by accommodating time-varying conversion…
Recurrent neural networks (RNNs) have long been an architecture of interest for computational models of human sentence processing. The recently introduced Transformer architecture outperforms RNNs on many natural language processing tasks…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
Multiple algorithms are known for efficiently calculating the prefix probability of a string under a probabilistic context-free grammar (PCFG). Good algorithms for the problem have a runtime cubic in the length of the input string. However,…
CPU scheduling is one of the most crucial operations performed by operating systems. Different conventional algorithms like FCFS, SJF, Priority, and RR (Round Robin) are available for CPU Scheduling. The effectiveness of Priority and Round…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in…
In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement…