Related papers: Towards a Definition of an Algorithm
Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…
We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a…
What is the best way to define algorithmic fairness? While many definitions of fairness have been proposed in the computer science literature, there is no clear agreement over a particular definition. In this work, we investigate ordinary…
The field of algorithmic optimization has significantly advanced with the development of methods for the automatic configuration of algorithmic parameters. This article delves into the Algorithm Configuration Problem, focused on optimizing…
The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
We can define a neural network that can learn to recognize objects in less than 100 lines of code. However, after training, it is characterized by millions of weights that contain the knowledge about many object types across visual scenes.…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Research software has been categorized in different contexts to serve different goals. We start with a look at what research software is, before we discuss the purpose of research software categories. We propose a multi-dimensional…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…
The problem of selecting an algorithm that appears most suitable for a specific instance of an algorithmic problem class, such as the Boolean satisfiability problem, is called instance-specific algorithm selection. Over the past decade, the…
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
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…