Related papers: When are two algorithms the same?
Intelligence can be defined as a predominantly human ability to accomplish tasks that are generally hard for computers and animals. Artificial Intelligence [AI] is a field attempting to accomplish such tasks with computers. AI is becoming…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
We revisit the foundations of fairness and its interplay with utility and efficiency in settings where the training data contain richer labels, such as individual types, rankings, or risk estimates, rather than just binary outcomes. In this…
A recent trend in mathematical modeling is to publish the computer code together with the research findings. Here we explore the formal question, whether and in which sense a computer implementation is distinct from the mathematical model.…
We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…
Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state…
The debate around bias in AI systems is central to discussions on algorithmic fairness. However, the term bias often lacks a clear definition, despite frequently being contrasted with fairness, implying that an unbiased model is inherently…
ASP programs are a convenient tool for problem solving, whereas with large problem instances the size of the state space can be prohibitive. We consider abstraction as a means of over-approximation and introduce a method to automatically…
Genetic algorithms are considered as an original way to solve problems, probably because of their generality and of their "blind" nature. But GAs are also unusual since the features of many implementations (among all that could be thought…
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…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
The study consists of two parts. Objective of the first part is modern language constructions responsible for algorithmically insolvability of parallelizing problem. Second part contains several ways to modify the constructions to make the…
The rapid growth of data in the recent years has led to the development of complex learning algorithms that are often used to make decisions in real world. While the positive impact of the algorithms has been tremendous, there is a need to…
I analyse differences in style between traditional prose mathematics writing and computer-formalised mathematics writing, presenting five case studies. I note two aspects where good style seems to differ between the two: in their…
Analogy-Based (or Analogical) and Case-Based Reasoning (ABR and CBR) are two similar problem solving processes based on the adaptation of the solution of past problems for use with a new analogous problem. In this paper we review these two…
In this paper, I put forward that in many instances, thinking mechanisms are equivalent to artificial intelligence modules programmed into the human mind.
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…