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- W1489719218 abstract "Via competing provers, we show that if a language A is selfreducible and has polynomial-size circuits then SA 2 = S2. Building on this, we strengthen the Kämper-AFK Theorem, namely, we prove that if NP ⊆ (NP ∩coNP)/poly then the polynomial hierarchy collapses to SNP∩coNP 2 . We also strengthen Yap’s Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to SNP 2 . Under the same assumptions, the best previously known collapses were to ZPPNP and ZPPNP NP respectively ([20],[6], building on [18,1,17,30]). It is known that S2 ⊆ ZPPNP [8]. That result and its relativized version show that our new collapses indeed improve the previously known results. Since the Kämper-AFK Theorem and Yap’s Theorem are used in the literature as bridges in a variety of results-ranging from the study of unique solutions to issues of approximation-our results implicitly strengthen all those results." @default.
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- W1489719218 date "2003-01-01" @default.
- W1489719218 modified "2023-10-16" @default.
- W1489719218 title "Competing Provers Yield Improved Karp-Lipton Collapse Results" @default.
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- W1489719218 doi "https://doi.org/10.1007/3-540-36494-3_47" @default.
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