A deterministic primality test with a polynomial time complexity of $\tilde{O}(\log^3(n))$ is presented. The test posits that an integer $n$ satisfying the conditions of the main theorem is prime. Combining elements of number theory and combinatorics, the proof operates on the basis of simultaneous modular congruences relating to binomial transforms ... more >>>

We give a new approach to the fundamental question of whether proof complexity lower bounds for concrete propositional proof systems imply super-polynomial Boolean circuit lower bounds.

For any poly-time computable function $f$, we define the witnessing formulas $w_n^k(f)$, which are propositional formulas stating that for any circuit $C$ of size ... more >>>

We study parallel repetition of k-player games where the constraints satisfy the projection property. We prove exponential decay in the value of a parallel repetition of projection games with value less than 1.

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