In this chapter, P, NP, and related complexity classes are defined, and the use of diagonalization and padding techniques to prove relationships between classes are illustrated, and it is shown how to prove that a problem is NP-complete.Expand

It is shown that the Euclidean traveling salesman problem lies in the counting hierarchy - the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE.Expand

It is shown that this natural complexity class for which the problems of determining if a system of linear equations is feasible and computing the rank of an integer matrix are complete under logspace reductions is closed under NC1-reducibility.Expand

30th Annual Symposium on Foundations of Computerâ€¦

30 October 1989

The author presents a very simple proof of the fact that any language accepted by polynomial-size depth-k unbounded-fan-in circuits of AND and OR gates is accepted by depth-three threshold circuitsâ€¦ Expand

It is shown that the permanent cannot be computed by uniform constantdepth threshold circuits of size T (n), for any function T such that for all k, T ( n) = o(2), and any problem that is hard for the complexity class C=P requires circuits of this size.Expand

This work analyzes the computational complexity of evaluating policies and of determining whether a sufficiently good policy exists for a Markov decision process, based on a number of confounding factors, including the observability of the system state; the succinctness of the representation; the type of policy; even the number of actions relative to theNumber of states.Expand

Proceedings 35th Annual Symposium on Foundationsâ€¦

20 November 1994

TLDR

A notion of resource-bounded measure for P and other subexponential-time classes is presented, based on Lutz's notion of measure, but overcomes the limitations that cause Lutzâ€™s definitions to apply only to classes at least as large as E.Expand