On the Structure and the Number of Prime Implicants of 2-CNFs

TL;DR

This paper investigates the maximum number of prime implicants in 2-CNF formulas, establishing tight bounds that grow exponentially with the number of variables, specifically around 3^{n/3}.

Contribution

It provides tight asymptotic bounds on the maximum number of prime implicants in 2-CNF formulas, advancing understanding of their structural complexity.

Findings

Maximum number of prime implicants in 2-CNF is approximately 3^{n/3}.

Established asymptotic bounds for m(n,2).

Results contribute to the theoretical understanding of 2-CNF formula complexity.

Abstract

Let $m(n, k)$ be the maximum number of prime implicants that any $k$-CNF on n variables can have. We show that $3^{n/3} \le m(n,2) \le (1+o(1))3^{n/3}$.