Devising an efficient deterministic – or even a nondeterministic sub-exponential time – algorithm for testing polynomial identities is a fundamental problem in algebraic comp...
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size ...
Randomness extractors convert weak sources of randomness into an almost uniform distribution; the conversion uses a small amount of pure randomness. In algorithmic applications, t...
Current formal models for quantum computation deal only with unitary gates operating on “pure quantum states”. In these models it is difficult or impossible to deal formally w...
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of no...