We present a new and conceptually simpler proof of a tight parallel-repetition theorem for public-coin arguments [Pass-Venkitasubramaniam, STOC’07], [Håstad et al, TCC’10], [Chung-Liu, TCC’10]. We follow the same proof framework as the previous non-tight parallel-repetition theorem of Håstad et al—which relied on
to measure the distance between experiments—and show that it can be made tight (and further simplified) if instead relying on
as the distance between the experiments.
We then use this new proof to present the first tight “Chernoff-type” parallel repetition theorem for arbitrary public-coin arguments, demonstrating that parallel-repetition can be used to simultaneously decrease both the soundness and completeness error of
public-coin argument at a rate matching the standard Chernoff bound.