Algorithmic randomness and computability theory inhabit a crossroads between mathematics and computer science, providing a rigorous framework for understanding randomness in infinite sequences and ...

A scientist from the Division of Quantum Condensed Matter Physics at the University of Tsukuba has formulated a new theory of superconductivity. Based on the calculation of the 'Berry connection', ...

Initially discussed are some of Alan Turing's wonderfully profound and influential ideas about mind and mechanism—including regarding their connection to the main topic of the present study, which is ...

We show that to every recursive total continuous functional Φ there is a PCF-definable representative Ψ of Φ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming ...

This course gives an introduction to the mathematical foundations of computation. The course will look at Turing machines, universal computation, the Church-Turing thesis, the halting problem and ...

This course gives an introduction to the mathematical foundations of computation. The course will look at Turing machines, universal computation, the Church-Turing thesis, the halting problem and ...