eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Reports
2192-5283
2017-09-18
89
101
10.4230/DagRep.7.2.89
article
Computability Theory (Dagstuhl Seminar 17081)
Ambos-Spies, Klaus
Brattka, Vasco
Downey, Rodney
Lempp, Steffen
Computability is one of the fundamental notions of mathematics and computer science, trying to capture the effective content of mathematics and its applications. Computability Theory explores the frontiers and limits of effectiveness and algorithmic methods. It has its origins in Gödel's Incompleteness Theorems and the formalization of computability by Turing and others, which later led to the emergence of computer science as we know it today. Computability Theory is strongly connected to other areas of mathematics and theoretical computer science. The core of this theory is the analysis of relative computability and the induced degrees of unsolvability; its applications are mainly to Kolmogorov complexity and randomness as well as mathematical logic, analysis and algebra. Current research in computability theory stresses these applications and focuses on algorithmic randomness, computable analysis, computable model theory, and reverse mathematics (proof theory). Recent advances in these research directions have revealed some deep interactions not only among these areas but also with the core parts of computability theory. The goal of this Dagstuhl Seminar is to bring together researchers from all parts of computability theory and related areas in order to discuss advances in the individual areas and the interactions among those.
https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume07/issue02/17081/DagRep.7.2.89/DagRep.7.2.89.pdf
algorithmic randomness
computability theory
computable algebra
computable analysis
generic case complexity
proof mining