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

Quantum theory describes events that take place on extremely short time scales. In the past, such events were regarded as 'momentary' or 'instantaneous': An electron orbits the nucleus of an atom—in ...

This year a series of events around the world will celebrate the work of Alan Turing, the father of the modern computer, as the 100th anniversary of his birthday approaches on June 23. In a book ...

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 ...

There is no doubt that water is significant. Without it, life would never have begun, let alone continue today—not to mention its role in the environment itself, with oceans covering over 70% of Earth ...

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 ...