Non-deterministic branching programs with logarithmic repetition cannot efficiently compute small monotone CNFs

Abstract

In this paper we establish an exponential lower bound on the size of syntactic non-deterministic read $d$-times branching programs for $d\le \log n/10^5$ computing a class of monotone CNFs with a linear number of clauses. This result provides the first separation of classes NP and co-NP for syntactic branching programs with a logarithmic repetition and the first separation of syntactic non-deterministic branching programs with a logarithmic repetition from small monotone CNFs.

Minor changes made in the abstract and the introduction in order to correct several inaccuracies in the informal statements