We consider the resolution proof complexity of propositional formulas which encode random instances of graph $k$-colorability. We obtain a tradeoff between the graph density and the resolution proof complexity.
For random graphs with linearly many edges we obtain linear-exponential lower bounds on the length of resolution refutations. For any $\epsilon>0$, ... more >>>

We study the power of balanced regular leaf-languages.
First, we investigate (i) regular languages that are
polylog-time reducible to languages in dot-depth 1/2 and
(ii) regular languages that are polylog-time decidable.
For both classes we provide

- forbidden-pattern characterizations, and
- characterizations in terms of regular expressions.

Both ... more >>>

A standard property testing algorithm is required to determine
with high probability whether a given object has property
P or whether it is \epsilon-far from having P, for any given
distance parameter \epsilon. An object is said to be \epsilon-far
from having ... more >>>