We present two new fundamental lower bounds on the worst-case combinatorial complexity of sets of free lines and sets of maximal free line segments in the presence of balls in thr...
This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy r...
or representation theory of groups), and even borrows abstract geometrical concepts like Euler characteristic or Grothendieck ring. However, the most stimulating for proof complexi...
We give the first time-space tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Reso...
—The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to...