Related papers: A Finite Soluble Quotient Algorithm

This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…

We present a new algorithm to decide finiteness of matrix groups defined over a field of positive characteristic. Together with previous work for groups in zero characteristic, this provides the first complete solution of the finiteness…

We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

The article presents an introductory review of quantum algorithms for non-relativisitc as well as relativistic four component molecular energy calculations developed in past few years.

We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or ${\mathcal N}$-constrained) groups.

We introduce the notion of a pro-fusion system on a pro-p group, which generalizes the notion of a fusion system on a finite p-group. We also prove a version of Alperin's Fusion Theorem for pro-fusion systems.

Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…

Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…

We investigate quantum inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the quantum…

In this note some properties of the sum of element orders of a finite abelian group are studied.

This paper concerns partial groups, objective partial groups, and (finite) localities, with special attention given to the quotient of a locality by a partial normal subgroup.

We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.

Let X(F,G) be the G-character variety of F where G is a rank 1 complex affine algebraic group and F is a finitely presentable discrete group. We describe an algorithm, which we implement in Mathematica, SageMath, and in Python, that takes a…

The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.

We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations…

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…

An efficient algorithm is presented for computation of the limit of exp(t A) for t towards infinity where A denotes an intensity matrix of finite dimension.