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Expander Construction in VNC1

Authors Sam Buss, Valentine Kabanets, Antonina Kolokolova, Michal Koucky

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Keywords
  • expander graphs
  • bounded arithmetic
  • alternating log time
  • sequent calculus
  • monotone propositional logic

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Abstract

We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson (2002), and show that this analysis can be formalized in the bounded arithmetic system VNC^1 (corresponding to the "NC^1 reasoning"). As a corollary, we prove the assumption made by Jerabek (2011) that a construction of certain bipartite expander graphs can be formalized in VNC^1. This in turn implies that every proof in Gentzen's sequent calculus LK of a monotone sequent can be simulated in the monotone version of LK (MLK) with only polynomial blowup in proof size, strengthening the quasipolynomial simulation result of Atserias, Galesi, and Pudlak (2002).

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Sam Buss, Valentine Kabanets, Antonina Kolokolova, and Michal Koucky. Expander Construction in VNC1. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 31:1-31:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ITCS.2017.31

Author Details

Sam Buss
Valentine Kabanets
Antonina Kolokolova
Michal Koucky

References

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