Publications [#348679] of Benjamin Rossman

Papers Published

1. Pitassi, T; Rossman, B; Tan, LY; Servedio, RA, Poly-logarithmic Frege depth lower bounds via an expander switching lemma, Proceedings of the Annual ACM Symposium on Theory of Computing, vol. 19-21-June-2016 (June, 2016), pp. 644-657, ISBN 9781450341325 [doi]
   (last updated on 2024/04/19)

   Abstract:
   We show that any polynomial-size Frege refutation of a certain linear-size unsatisfiable 3-CNF formula over n variables must have depth Ω(√logn). This is an exponential improvement over the previous best results (Pitassi et al. 1993, Krajíček et al. 1995, Ben-Sasson 2002) which give Ω(log log n) lower bounds. The 3-CNF formulas which we use to establish this result are Tseitin contradictions on 3-regular expander graphs. In more detail, our main result is a proof that for every d, any depth-d Frege refutation of the Tseitin contradiction over these n-node graphs must have size nΩ(logn n)/d2). A key ingredient of our approach is a new switching lemma for a carefully designed random restriction process over these expanders. These random restrictions reduce a Tseitin instance on a 3-regular n-node expander to a Tseitin instance on a random subgraph which is a topological embedding of a 3-regular n'-node expander, for some n' which is not too much less than n. Our result involves Ω(√logn) iterative applications of this type of random restriction.