A fundamental question in complexity theory is whether every randomized polynomial time algorithm can be simulated by a deterministic polynomial time algorithm (that is, whether B...
Abstract. Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with b...
We study the extension (introduced as BT in [5]) of the theory S1 2 by instances of the dual (onto) weak pigeonhole principle for p-time functions, dWPHP(PV )x x2 . We propose a n...
We present an alternate proof of the recent result by Gutfreund and Kawachi that derandomizing Arthur-Merlin games into PNP implies linear-exponential circuit lower bounds for ENP...
Scott Aaronson, Baris Aydinlioglu, Harry Buhrman, ...
We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NP-complete in the Blum-Shub-Smale mo...