Polynomial Closure

Polynomial Closure and Topology

Power Semigroups and Polynomial Closure

Truth-table Closure and Turing Closure of Average Polynomial Time have Different Measures in EXP

Let P P-comp denote the sets that are solvable in polynomial time on average under every polynomial-time computable distribution on the instances. In this paper we show that the truth-table closure of P P-comp has measure 0 in EXP. Since, as we show, EXP is Turing reducible to P P-comp , the Turing closure has measure 1 in EXP and thus, P P-comp is an example of a subclass of E such that the cl...

Hermite Polynomial Closure Approximations for Stochastic Epidemic Models

Moment closure approximations have been developed to provide simple approximations to non-linear stochastic models. They can give tremendous insight into the qualitative and quantitative behavior of stochastic models. They are also important because they can be used to mimic behavior observed in simulation studies, or in some cases, validate the dynamics of rigorous limit theorems. In most stoc...

Some Closure Results for Polynomial Factorization and Applications

In a sequence of fundamental results in the 80’s, Kaltofen [Kal85, Kal86, Kal87, Kal89] showed that factors of multivariate polynomials with small arithmetic circuits have small arithmetic circuits. In other words, the complexity class VP is closed under taking factors. A natural question in this context is to understand if other natural classes of multivariate polynomials, for instance, arithm...