Competing provers yield improved Karp-Lipton collapse results

Jin Yi Cai, Venkatesan T. Chakaravarthy, Lane A. Hemaspaandra, Mitsunori Ogihara

Research output: Contribution to journalArticle

5 Scopus citations


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 [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.

Original languageEnglish (US)
Pages (from-to)535-546
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - Dec 1 2003
Externally publishedYes


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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