Verifying Proofs in Constant Depth

  • Olaf Beyersdorff
  • Samir Datta
  • Meena Mahajan
  • Gido Scharfenberger-Fabian
  • Karteek Sreenivasaiah
  • Michael Thomas
  • Heribert Vollmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)


In this paper we initiate the study of proof systems where verification of proofs proceeds by \(\protect{\ensuremath{\mathsf{NC}}}^{0}\) circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by \(\protect{\ensuremath{\mathsf{NC}}}^{0}\) functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct \(\protect{\ensuremath{\mathsf{NC}}}^{0}\) proof systems for a variety of languages ranging from regular to \(\protect{\ensuremath{\mathsf{NP}}}\)-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit \(\protect{\ensuremath{\mathsf{NC}}}^{0}\) proof systems. We also present a general construction of \(\protect{\ensuremath{\mathsf{NC}}}^{0}\) proof systems for regular languages with strongly connected NFA’s.


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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Olaf Beyersdorff
    • 1
  • Samir Datta
    • 2
  • Meena Mahajan
    • 3
  • Gido Scharfenberger-Fabian
    • 4
  • Karteek Sreenivasaiah
    • 3
  • Michael Thomas
    • 5
  • Heribert Vollmer
    • 1
  1. 1.Institut für Theoretische InformatikLeibniz Universität HannoverGermany
  2. 2.Chennai Mathematical InstituteIndia
  3. 3.Institute of Mathematical SciencesChennaiIndia
  4. 4.Institut für Mathematik und InformatikErnst-Moritz-Arndt-UniversitätGreifswaldGermany
  5. 5.TWT GmbHNeuhausen a. d. F.Germany

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