Tricritical Points in Random Combinatorics: the (2+p)-SAT case

TL;DR

This paper analytically identifies a tricritical point in the phase diagram of the random (2+p)-SAT problem, enhancing understanding of phase transitions in random combinatorics and complexity theory.

Contribution

It analytically computes the tricritical point in the (2+p)-SAT problem's phase diagram using the replica method, providing bounds consistent with prior numerical and rigorous results.

Findings

Tricritical point bounds: 0.4 to 0.416

Analytical approach confirms previous simulations

Enhances understanding of phase transitions in random SAT

Abstract

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a tricritical point in the phase diagram of the random $2+p$-SAT problem is analytically computed using the replica approach and found to lie in the range $2/5 \le p_0 \le 0.416$. These bounds on $p_0$ are in agreement with previous numerical simulations and rigorous results.