We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n points in IRd is simplicial, or to determine the number ...
Abstract. In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functio...
The P vs NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We do not know if even a slight algorithmic imp...
We prove new lower bounds for locally decodable codes and private information retrieval. We show that a 2-query LDC encoding nbit strings over an ℓ-bit alphabet, where the decode...
A q-ary error-correcting code C ⊆ {1, 2, . . . , q}n is said to be list decodable to radius ρ with list size L if every Hamming ball of radius ρ contains at most L codewords o...