Related papers: Computability and analysis: the legacy of Alan Tur…
We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related…
The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…
Artificial intelligence (AI) is an emerging technology that has the potential to transform many aspects of society, including the economy, healthcare, and transportation. This article synthesizes recent research literature on the global…
Ancestry and genealogy tree are proven tools to determine the lineage of any person and establish dependencies among individuals. Genealogy tree can be exploited further to gain information about the researcher and his scholastic lineage…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
The paper describes the contributions of Alain Colmerauer to the areas of logic programs (LP) and constraint logic programs (CLP).
This article presents a survey of computability logic: its philosophy and motivations, main concepts and most significant results obtained so far. A continuously updated online version of this article is maintained at…
Advances in artificial intelligence (AI) will transform many aspects of our lives and society, bringing immense opportunities but also posing significant risks and challenges. The next several decades may well be a turning point for…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The introduction of generative artificial intelligence applications to the public has led to heated discussions about its potential impacts and risks for K-12 education. One particular challenge has been to decide what students should learn…
We introduce an analog of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time…
This paper proposes a specific conceptualization of intelligence as computation. This conceptualization is intended to provide a unified view for all disciplines of intelligence research. Already, it unifies several conceptualizations…
Text-based personality computing (TPC) has gained many research interests in NLP. In this paper, we describe 15 challenges that we consider deserving the attention of the research community. These challenges are organized by the following…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize Gudhi library. It is under constant development, so please do not consider this…
Non standard analysis is an area of Mathematics dealing with notions of infinitesimal and infinitely large numbers, in which many statements from classical analysis can be expressed very naturally. Cheap non-standard analysis introduced by…
We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…
Modern society is permeated with computers, and the software that controls them can have latent, long-term, and immediate effects that reach far beyond the actual users of these systems. This places researchers in Computer Science and…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…