2 citations · 3 across the 12 of their papers we have counts for
15 papers
On Word Representations and Embeddings in Complex Matrices
Paul C. Bell, George Kenison, Reino Niskanen +2
Embeddings of word structures into matrix semigroups provide a natural bridge between combinatorics on words and linear algebra. However, low-dimensional matrix semigroups impose s…
On the growth of hypergeometric sequences
George Kenison, Jakub Konieczny, Florian Luca +3
Hypergeometric sequences obey first-order linear recurrence relations with polynomial coefficients and are commonplace throughout the mathematical and computational sciences. For c…
Simple Linear Loops: Algebraic Invariants and Applications
Rida Ait El Manssour, George Kenison, Mahsa Shirmohammadi +1
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted c…
Determination Problems for Orbit Closures and Matrix Groups
Rida Ait El Manssour, George Kenison, Mahsa Shirmohammadi +2
Computational problems concerning the orbit of a point under the action of a matrix group occur throughout computer science, including in program analysis, complexity theory, quant…
Linear Loop Synthesis for Quadratic Invariants
S. Hitarth, George Kenison, Laura Kovács +1
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task a…
(Un)Solvable Loop Analysis
Daneshvar Amrollahi, Ezio Bartocci, George Kenison +3
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the…
The Membership Problem for Hypergeometric Sequences with Quadratic Parameters
George Kenison, Klara Nosan, Mahsa Shirmohammadi +1
Hypergeometric sequences are rational-valued sequences that satisfy first-order linear recurrence relations with polynomial coefficients; that is, a hypergeometric sequence $\langl…
From Polynomial Invariants to Linear Loops
George Kenison, Laura Kovács, Anton Varonka
Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verific…
The Threshold Problem for Hypergeometric Sequences with Quadratic Parameters
George Kenison
Hypergeometric sequences are rational-valued sequences that satisfy first-order linear recurrence relations with polynomial coefficients; that is, $\langle u_n \rangle_{n=0}^\infty…
Solving Invariant Generation for Unsolvable Loops
Daneshvar Amrollahi, Ezio Bartocci, George Kenison +3
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the…
On the Skolem Problem for Reversible Sequences
George Kenison
Given an integer linear recurrence sequence , the Skolem Problem asks to determine whether there is a natural number such that . Recent work by…
On Positivity and Minimality for Second-Order Holonomic Sequences
George Kenison, Oleksiy Klurman, Engel Lefaucheux +5
An infinite sequence of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with p…
On the Skolem Problem and Prime Powers
George Kenison, Richard Lipton, Joël Ouaknine +1
The Skolem Problem asks, given a linear recurrence sequence , whether there exists such that . In this paper we consider the following specialisation…
Statistics in conjugacy classes in free groups
George Kenison, Richard Sharp
In this paper, we establish statistical results for a convex co-compact action of a free group on a CAT() space where we restrict to a non-trivial conjugacy class in the group.…
Orbit counting in conjugacy classes for free groups acting on trees
George Kenison, Richard Sharp
In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each…