A hitting-set generator is a deterministic algorithm that generates a set of strings such that this set intersects every dense set that is recognizable by a small circuit. A polynomial time hitting-set generator readily implies RP = P , but it is not apparent what this implies for BPP. Nevertheless, Andreev et al. (ICALP’96, and JACM 1998) showed that a polynomial-time hitting-set generator imp...

A hitting-set generator is a deterministic algorithm which generates a set of strings that intersects every dense set recognizable by a small circuit. A polynomial time hitting-set generator readily implies $RP=P$. Andreev et. Al (ICALP’96 and JACM 1998) showed that if polynomial-time hitting-set generator in fact implies the much stronger conclusion $BPP=P$. We simplify and improve their (and ...

We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size (nw)O(logn) where n is the number of variables and w is the width of the ROABP. Even for a constantwidth ROABP, nothing better than a quasi-polynomial bound ...

Let A = {a1, . . . , an} be a set and F = {F1, . . . , Fm} a family of subsets of A. A subset H ⊆ A has the hitting set property, or is a hitting set, iff H ∩ Fi 6= ∅ for 1 ≤ i ≤ m (i.e., H “hits” each set Fi). If we are given a cost function c : A → N, the cost of H is ∑ a∈H c(a). A hitting set is of minimum cost if its cost is minimal among all hitting sets. The problem of finding a minimum-c...

The hitting time Hxy between two vertices x and y of a graph is the average time that the standard simple random walk takes to get from x to y. In this paper, we study the distribution of the hitting time between two randomly chosen vertices of a random tree. We consider both uniformly random labelled trees and a more general model with vertex weights akin to simply generated trees. We show tha...