Multiplicity Problems on Algebraic Series and Context-Free Grammars

In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polynomial equations: a formalism closely related to weighted context-free grammars. We focus on three problems -- decide whether a given algebraic series is identically zero, determine whether all but finitely many coefficients are zero, and compute the coefficient of a specific monomial. We relate these questions to well-known computational problems on arithmetic circuits and thereby show that all three problems lie in the counting hierarchy. Our main result improves the best known complexity bound on deciding zeroness of an algebraic series. This problem is known to lie in PSPACE by reduction to the decision problem for the existential fragment of the theory of real closed fields. Here we show that the problem lies in the counting hierarchy by reduction to the problem of computing the degree of a polynomial given by an arithmetic circuit. As a corollary we obtain new complexity bounds on multiplicity equivalence of context-free grammars restricted to a bounded language, language inclusion of a nondeterministic finite automaton in an unambiguous context-free grammar, and language inclusion of a non-deterministic context-free grammar in an unambiguous finite automaton.Comment: full technical report of a LICS'23 pape

On the Computation of the Algebraic Closure of Finitely Generated Groups of Matrices

We investigate the complexity of computing the Zariski closure of a finitely generated group of matrices. The Zariski closure was previously shown to be computable by Derksen, Jeandel, and Koiran, but the termination argument for their algorithm appears not to yield any complexity bound. In this paper we follow a different approach and obtain a bound on the degree of the polynomials that define the closure. Our bound shows that the closure can be computed in elementary time. We also obtain upper bounds on the length of chains of linear algebraic groups, where all the groups are generated over a fixed number field

Engineering of an object-counting program

Counting objects in images is an important problem in many fields, such as the field of life sciences, where counting cells in microscopic images is a fundamental analysis tool. In this Bachelor's Thesis we present ImageJ, the state of the art program for microscopic image processing in life sciences. We provide an overview of the newest version of ImageJ with an emphasis on the architecture and the API of the software. We present Learn123, a program designed to automize cell counting in microscopic images using ImageJ. We describe the process of updating Learn123 by using the most recent version of ImageJ and parallelizing the genetic algorithm used to learn cell counting. We then compare the parallel algorithm to its previous sequential version. Finally, we present a new use case of Learn123 and discuss which types of images are not suitable for object counting using ImageJ

DEVELOPING SOFTWARE APPLICATIONS FOR BE-OP-ISO

The on-line isotope mass separator ISOLDE is a facility dedicated to the production of a large variety of radioactive ion beams for many different experiments in the fields of nuclear and atomic physics, solid-state physics, materials science and life sciences. The ISOLDE section of the Operations group is responsible for operating the facility, notably setting up and monitoring the running of the machine in order to enable the users to perform their experiments. The operators’ work also includes maintaining operation schedules, collaborating with the physics coordinator regarding the physics schedule, preparation of operational procedures, providing beam statistics and writing software applications to control the facility [2], the last of which is also what I did as part of the CERN Summer Student Programme. My work comprised both of consolidating existing software and working on a new project that is in the process of being put into regular use