Constant-Round Interactive Proof Systems for AC0[2] and NC1
Abstract: We present constant-round interactive proof systems for sufficiently uniform versions of \(\mathcal{AC}^0[2]\) and \(\mathcal{NC}^1\). Both proof systems are doubly-efficient, and offer a better trade-off between the round complexity and the total communication than the work of Reingold, Rothblum, and Rothblum (STOC, 2016). Our proof system for \(\mathcal{AC}^0[2]\) supports a more relaxed notion of uniformity and offers a better trade-off between the number of rounds and the round complexity that our proof system for \(\mathcal{NC}^1\). We observe that all three aforementioned systems yield constant-round doubly-efficient proof systems for the All-Pairs Shortest Paths problem.
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