Expander Construction in VNC1

We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [38], and show that this analysis can be formalized in the bounded-arithmetic system VNC1 (corresponding to the “NC1 reasoning”). As a corollary, we prove the assumption made by Jeřábek [24] that a construction of certain bipartite expander graphs can be formalized in VNC1. 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 Pudlák [7]. 1998 ACM Subject Classification F.4.1 Mathematical Logic, F.2.1 Numerical Algorithms and Problems, F.1.3 Complexity Measures and Classes