Kai-Min Chung, Feng-Hao Liu

Following Hastad, Pass, Pietrzak, and Wikstrom (2008), we study parallel repetition theorems for public-coin interactive arguments and their generalization. We obtain the following results:

1. We show that the reduction of Hastad et al. actually gives a tight direct product theorem for public-coin interactive arguments. That is, $n$-fold parallel repetition ... more >>>

VyasRam Selvam

We explore the implications of the two queries assumption, $P^{NP[1]}=P_{||}^{NP[2]}$, with respect to the polynomial hierarchy and the classes $AM$ and $MA$.

We prove the following results:

1. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $AM = MA$

2. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $PH \subset MA_{/1}$

3. $\exists\;B\;P^{NP[1]^B}=P^{NP[2]^B}$ and $NP^B \not\subseteq coMA^B$.

4. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $PH ...
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Scott Aaronson, Russell Impagliazzo, Dana Moshkovitz

We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close ... more >>>

Zeyu Guo, Nitin Saxena, Amit Sinhababu

Testing whether a set $\mathbf{f}$ of polynomials has an algebraic dependence is a basic problem with several applications. The polynomials are given as algebraic circuits. Algebraic independence testing question is wide open over finite fields (Dvir, Gabizon, Wigderson, FOCS'07). The best complexity known is NP$^{\#\rm P}$ (Mittmann, Saxena, Scheiblechner, Trans.AMS'14). ... more >>>