Computability theory establishes which problems can in principle be solved by mechanical procedures, formalised by the Turing machine model and its equivalents. It draws a firm boundary between ...

Computational complexity theory examines the intrinsic difficulty of algorithmic problems by classifying them into hierarchies according to the resources—typically time and space—required for their ...

A major advance reveals deep connections between the classes of problems that computers can — and can’t — possibly do. At first glance, the big news coming out of this summer’s conference on the ...