polynomial-time reducibilityWe investigate the question of whether one can characterize complexity classes (such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorov-random strings R K . We show that this question cannot be posed without explicitly dealing with issues ...
This special case of the Hilbert-Smith conjecture (or more precisely, a generalisation thereof in which “finite-dimensional manifold” was replaced by “locally connected locally compact finite-dimensional”) was used in Gromov’s proof of his famous theorem on groups of polynomial growth. I ...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I ar...
Any decidable set that is polynomial-time monotone-truth-table reducible to R C is in P / poly. Any decidable set that is polynomial-time truth-table reducible to R C via a reduction that asks at most f ( n ) queries on inputs of size n lies in P / ( f ( n ) 2 f ( n ...