Document Open Access Logo

Finding Irrefutable Certificates for S_2^p via Arthur and Merlin

Authors Venkatesan T. Chakaravarthy, Sambuddha Roy



PDF
Thumbnail PDF

File

LIPIcs.STACS.2008.1342.pdf
  • Filesize: 182 kB
  • 12 pages

Document Identifiers

Author Details

Venkatesan T. Chakaravarthy
Sambuddha Roy

Cite AsGet BibTex

Venkatesan T. Chakaravarthy and Sambuddha Roy. Finding Irrefutable Certificates for S_2^p via Arthur and Merlin. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 157-168, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.STACS.2008.1342

Abstract

We show that $S_2^psubseteq P^{prAM}$, where $S_2^p$ is the symmetric alternation class and $prAM$ refers to the promise version of the Arthur-Merlin class $AM$. This is derived as a consequence of our main result that presents an $FP^{prAM}$ algorithm for finding a small set of ``collectively irrefutable certificates'' of a given $S_2$-type matrix. The main result also yields some new consequences of the hypothesis that $NP$ has polynomial size circuits. It is known that the above hypothesis implies a collapse of the polynomial time hierarchy ($PH$) to $S_2^psubseteq ZPP^{NP}$ (Cai 2007, K"obler and Watanabe 1998). Under the same hypothesis, we show that $PH$ collapses to $P^{prMA}$. We also describe an $FP^{prMA}$ algorithm for learning polynomial size circuits for $SAT$, assuming such circuits exist. For the same problem, the previously best known result was a $ZPP^{NP}$ algorithm (Bshouty et al. 1996).
Keywords
  • Symmetric alternation
  • promise-AM
  • Karp--Lipton theorem
  • learning circuits

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail