John Gill

TL;DR: Relativized versions of the open question of whether every language accepted nondeterministically in polynomial time can be recognized deterministic in poynomial time are investigated.

TL;DR: It is shown that every nondeterministic machine can be simulated in the same space by a probabilistic machine with small error probability.

TL;DR: It is shown how probabilisticlinear-bounded automata can simulate nondeterministic linear-bounding automata and an example is given of a function computable more quickly by Probabilistic Turing machines than by deterministic Turing machines.

TL;DR: Let A be a language chosen randomly by tossing a fair coin for each string x to determine whether x belongs to A, and${\bf NP}^A is shown, with probability 1, to contain a-immune set, i.e., a set having no infinite subset in ${\bf P]^A $.

TL;DR: The question of how much space is needed to represent a set is considered, given a finite universe U and some subset V and a procedure that for each element s in U determines if s is in V.