In computational complexity theory, P and NP are two classes of problems. P is the class of decision problems that a deterministic Turing machine can solve in polynomial time. In useful terms, any ...

The prolific researcher found deep connections between randomness and computation and spent a career influencing cryptographers, complexity researchers and more. For more than 40 years, Avi Wigderson ...

Vol. 95, No. 1/2, The Contributions of Logic to the Foundations of Physics (June/July 2010), pp. 279-300 (22 pages) Earlier, we have studied computations possible by physical systems and by algorithms ...

Computational complexity and computability are central themes in theoretical computer science that address the fundamental question of what can be computed and at what cost. Computability theory ...

Since the 1930s, the theory of computation has profoundly influenced philosophical thinking about topics such as the theory of the mind, the nature of mathematical knowledge and the prospect of ...

In this paper I discuss the topics of mechanism and algorithmicity. I emphasise that a characterisation of algorithmicity such as the Turing machine is iterative; and I argue that if the human mind ...

Alex Smith, a 20-year-old British engineering student, has proved that a Turing machine proposed by complexity guru Stephen Wolfram is in fact the simplest possible computer capable of solving every ...

Charles Darwin and Alan Turing, in their different ways, both homed in on the same idea: the existence of competence without comprehension. Some of the greatest, most revolutionary advances in science ...