Related papers: Deciding Confluence and Normal Form Properties of …
The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep…
The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…
We describe a matrix multiplication recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time $O(n^{\omega d})$ where $M(m) = O(m^{\omega})$ is the running time for $m \times m$ matrix…
This paper describes experiments showing that some tasks in natural language processing (NLP) can already be performed using quantum computers, though so far only with small datasets. We demonstrate various approaches to topic…
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem.…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewriting formalisms, it guarantees that the computations are not dependent on rule application order, and also because it implies the logical…
In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…
Sequence prediction and classification are ubiquitous and challenging problems in machine learning that can require identifying complex dependencies between temporally distant inputs. Recurrent Neural Networks (RNNs) have the ability, in…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
Time, cost, and energy efficiency are critical considerations in Deep-Learning (DL), particularly when processing long texts. Transformers, which represent the current state of the art, exhibit quadratic computational complexity relative to…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
For years, recursive neural networks (RvNNs) have been shown to be suitable for representing text into fixed-length vectors and achieved good performance on several natural language processing tasks. However, the main drawback of RvNNs is…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
Computational cognitive modeling investigates human cognition by building detailed computational models for cognitive processes. Adaptive Control of Thought - Rational (ACT-R) is a rule-based cognitive architecture that offers a widely…
In this paper, we introduce a restriction of Timed Automata (TA), called non-resetting test Timed Automata (nrtTA). An nrtTA does not allow to test and reset the same clock on the same transition. The model has the same expressive power of…
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to some random subspace of the parameters, constructing and…
In this paper we investigate convergent term rewriting systems that conform to the criteria set out by Christopher Lynch and Barbara Morawska in their seminal paper "Basic Syntactic Mutation." The equational unification problem modulo such…