Diagonalizations over polynomial time computable sets

A Thirty Year Old Conjecture about Promise Problems

“…Measured in terms of the length of x, this time is roughly t(|x| + 2 |x| ). The notion of unpredictability is very similar to the notion of genericity [ASFH87,ASNT96]. In fact it is known that for deterministic computations, these two notions are equivalent [BM95].…”

“…This hypothesis is shown to have several interesting and believable consequences [ASFH87] [ASNT96]. In the definition of unpredictability, if we replace strong nondeterministic machines by deterministic machines, then it coincides with genericity [BM95].…”

Feasible Analysis, Randomness, and Base Invariance

“…Recall the definition of occ σ (τ ) in (1). Let c ∈ Σ r and α ∈ Σ * r such that α c is a string of minimal length for which it is not the case that lim n→∞ occ α c (Z n )/n = r −|α|−1 .…”

“…(By a result of Schnorr, restricting to rational values is immaterial.) We say that Z is polynomial time random if Z is n c -random for every c, that is, no polynomial time martingale succeeds on Z. Polynomial time random sequences have been studied for instance in [3], where some connections to Lutz's polynomial time bounded measure [16,17] and polynomial genericity [1,2] are discussed.…”

Genericity and measure for exponential time

“…[ 11,[13][14][15][16][17][18]201) used this concept to investigate the quantitative structure of Exponential Time (E = DTIME(2"")). Previously, Ambos-Spies et al [2,3] introduced polynomial time bounded genericity concepts and used them for the investigation of structural properties of NP (under appropriate assumptions) and E. Here we relate these concepts to each other. We show that, for any c 3 1, the class of n'-generic sets has p-measure 1.…”