Fri, 24 November 2017
In this episode we discuss the complexity class of EXP-Time which contains algorithms which require $O(2^{p(n)})$ time to run. In other words, the worst case runtime is exponential in some polynomial of the input size. Problems in this class are even more difficult than problems in NP since you can't even verify a solution in polynomial time. We mostly discuss Generalized Chess as an intuitive example of a problem in EXP-Time. Another well-known problem is determining if a given algorithm will halt in k steps. That extra condition of restricting it to k steps makes this problem distinct from Turing's original definition of the halting problem which is known to be intractable. |