Under the Strong Exponential Time Hypothesis, simulation preorder and simulation equivalence cannot be decided in O(n^{2-epsilon}) time, so simulation is inherently quadratic.
Simulation-based minim azation
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A Quadratic Lower Bound for Simulation
Under the Strong Exponential Time Hypothesis, simulation preorder and simulation equivalence cannot be decided in O(n^{2-epsilon}) time, so simulation is inherently quadratic.