Related papers: When are two algorithms the same?
Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
Machines have achieved a broad and growing set of linguistic competencies, thanks to recent progress in Natural Language Processing (NLP). Psychologists have shown increasing interest in such models, comparing their output to psychological…
In the field of algorithmic fairness, many fairness criteria have been proposed. Oftentimes, their proposal is only accompanied by a loose link to ideas from moral philosophy -- which makes it difficult to understand when the proposed…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
The notion that algorithmic systems should be "transparent" and "explainable" is common in the many statements of consensus principles developed by governments, companies, and advocacy organizations. But what exactly do policy and legal…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
Was it fair that Harry was hired but not Barry? Was it fair that Pam was fired instead of Sam? How can one ensure fairness when an intelligent algorithm takes these decisions instead of a human? How can one ensure that the decisions were…
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness…
Fairness concerns about algorithmic decision-making systems have been mainly focused on the outputs (e.g., the accuracy of a classifier across individuals or groups). However, one may additionally be concerned with fairness in the inputs.…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
Discussions of algorithmic bias tend to focus on examples where either the data or the people building the algorithms are biased. This gives the impression that clean data and good intentions could eliminate bias. The neutrality of the…
An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…
Computer programs are part of our daily life, we use them, we provide them with data, they support our decisions, they help us remember, they control machines, etc. Programs are made by people, but in most cases we are not their authors, so…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…