A Hike in the Phases of the 1-in-3 Satisfiability

TL;DR

This paper investigates the phase transitions in the random epsilon-1-in-3 satisfiability problem, analyzing how negation probability affects the problem's solvability and computational hardness using both rigorous and heuristic approaches.

Contribution

It provides a comprehensive analysis of SAT/UNSAT and hardness transitions in the epsilon-1-in-3 SAT problem, combining rigorous proofs with heuristic insights.

Findings

Identifies the critical thresholds for SAT/UNSAT transitions.

Characterizes the hardness landscape across different negation probabilities.

Provides both theoretical and heuristic descriptions of phase transitions.

Abstract

We summarise our results for the random $\epsilon$--1-in-3 satisfiability problem, where $\epsilon$ is a probability of negation of the variable. We employ both rigorous and heuristic methods to describe the SAT/UNSAT and Hard/Easy transitions.