Devising an efficient deterministic – or even a nondeterministic sub-exponential time – algorithm for testing polynomial identities is a fundamental problem in algebraic comp...
We introduce a new encoding of the face numbers of a simplicial complex, its Stirling polynomial, that has a simple expression obtained by multiplying each face number with an app...
Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an add...
We obtain two results about the proof complexity of deep inference: 1) deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin exte...
We present an alternate proof of the result by Kabanets and Impagliazzo that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales b...