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

TL;DR

This paper proves an exponential size lower bound for non-deterministic branching programs with logarithmic repetition computing certain monotone CNFs, establishing new complexity class separations.

Contribution

It introduces the first exponential lower bound for such branching programs on monotone CNFs and separates NP from co-NP in this context.

Findings

Exponential lower bound on branching program size for monotone CNFs

First separation of NP and co-NP for these branching programs

Demonstrates limitations of non-deterministic branching programs with logarithmic repetition

Abstract

In this paper we establish an exponential lower bound on the size of syntactic non-deterministic read $d$-times branching programs for $d \leq \log n /10^5$ 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.