A Quadratic Lower Bound for Simulation

TL;DR

This paper proves that deciding simulation equivalence and preorder inherently require quadratic time, establishing a fundamental computational complexity barrier assuming the Strong Exponential Time Hypothesis.

Contribution

It provides the first quadratic lower bounds for simulation problems, showing they are inherently as hard as the best known quadratic algorithms.

Findings

Deciding simulation equivalence has quadratic lower bounds.

Simulation is inherently harder than bisimilarity.

Supports the quadratic upper bounds with a matching lower bound.

Abstract

We show that deciding simulation equivalence and simulation preorder have quadratic lower bounds assuming that the Strong Exponential Time Hypothesis holds. This is in line with the best know quadratic upper bounds of simulation equivalence. This means that deciding simulation is inherently quadratic. A typical consequence of this result is that computing simulation equivalence is fundamentally harder than bisimilarity.