Related papers: Algorithmic information theory: Some recollections
This paper presents a detailed case study of how artificial intelligence, especially large language models, can be integrated into historical research workflows. The workflow is divided into nine steps, covering the full research cycle from…
In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…
This paper describes serial and parallel compositional models of multiple objects with part sharing. Objects are built by part-subpart compositions and expressed in terms of a hierarchical dictionary of object parts. These parts are…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
In the last couple of years we have witnessed an enormous increase of machine learning (ML) applications. More and more program functions are no longer written in code, but learnt from a huge amount of data samples using an ML algorithm.…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…
This paper applies Algorithmic Information Theory to simple examples of replication processes to illustrate how replicating structures can generate and maintain order in a non equilibrium system. Variation in replicating structures enhances…
The main result is that: function descriptions are not made equal, and they can be categorised in at least two categories using various computational methods for function evaluation. The result affects Kolmogorov complexity and Random…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
We have been involved in the creation of multiple software systems for computer algebra, including Reduce, Maple, Axiom and Aldor as well as a number of smaller specialised programs. We relate observations on how the meaning of software…
Supercompilation is a powerful program transformation technique with numerous interesting applications. Existing methods of supercompilation, however, are often very unpredictable with respect to the size of the resulting programs. We…
This paper gives a brief description of the author's database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned.
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series…