On alternation II

Abstract

Every deterministic t(n)-time bounded multitape Turing machine can be simulated by an alternating t(n) loglog t(n)/log t(n)-time bounded Turing machine. If the depth of every directed acyclic graph with n edges can be reduced to log n by removing only o(n) edges, then in linear time nondeterministic multitape Turing machines can recognize mor languages than deterministic multitape Turing machines. For some graphs reduction of the depth to log n requires the removal of Ω(n/loglog n) edges. A graph theoretic condition is given, which implies that obliviousness reduces the power of multitape Turing machines.