An approximate membership data structure is a randomized data
structure for representing a set which supports membership
queries. It allows for a small false positive error rate but has
no false negative errors. Such data structures were first
introduced by Bloom in the 1970's, and have since had numerous
applications, ... more >>>

In an unpublished Russian manuscript Razborov proved that a matrix family with high
rigidity over a finite field would yield a language outside the polynomial hierarchy
in communication complexity.

We present an alternative proof that strengthens the original result in several ways.
In particular, we replace rigidity by the strictly ... more >>>

It has been observed empirically that clause learning does not significantly improve the performance of a SAT solver when restricted
to learning clauses of small width only. This experience is supported by lower bound theorems. It is shown that lower bounds on the runtime of width-restricted clause learning follow from ... more >>>