Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication

TL;DR

This paper proves that identifying a falsified clause in a random unsatisfiable CNF with logarithmic clauses requires linear communication, highlighting the problem's computational hardness in a randomized setting.

Contribution

It establishes a linear lower bound on the randomized communication complexity for falsified clause detection in random log n-CNFs, a previously unexplored hardness result.

Findings

Linear communication complexity lower bound proven

Hardness result for randomized algorithms in clause falsification

Insights into complexity of satisfiability problems in random CNFs

Abstract

We show that for a randomly sampled unsatisfiable $O(\log n)$-CNF over $n$ variables the randomized two-party communication cost of finding a clause falsified by the given variable assignment is linear in $n$.