Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2A = 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 S2NP∩coNP. We also strengthen Yap's Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to S2NP. Under the same assumptions, the best previously known collapses were to ZPPNP and ZPPNPNP respectively ([20,6], building on [18,1,17,30]). It is known that S2 ⊆ ZPPNP . 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.
|Original language||English (US)|
|Number of pages||12|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|State||Published - Dec 1 2003|
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)