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 ...

Theory of Computation offers a rigorous mathematical framework that underpins our understanding of what can be computed and how efficiently these computations may be performed. It encompasses ...

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 ...

While the invention of calculus by Newton and Leibniz in the 17th century set the stage for the so-called industrial revolution and unleashed unparalleled analytical power to fast-track human ...

On Saturday, British mathematician Alan Turing would have turned 100 years old. It is barely fathomable to think that none of the computing power surrounding us today was around when he was born. But ...