In this paper we investigate the question whether a perfect matching can be isolated by a weighting scheme
using Chinese Remainder Theorem (short: CRT). We give a systematical analysis to a method based on CRT
suggested by Agrawal in a CCC'03-paper
for testing perfect matchings. We show that ... more >>>

The existence of an optimal propositional proof system is a major open question in proof complexity; many people conjecture that such systems do not exist. Krajicek and Pudlak (1989) show that this question is equivalent to the existence of an algorithm that is optimal on all propositional tautologies. Monroe (2009) ... more >>>

We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating a height $h$ formulae, we prove a lower bound for the $\delta$-two-sided-error randomized decision tree complexity of $(1-2\delta)(5/2)^h$, improving the lower bound of $(1-2\delta)(7/3)^h$ given by Jayram et al. (STOC '03). We also state a conjecture ... more >>>