Extending Two-Part Epiplexity to Generalized Epiplexity

Avg Correlation

Two-Part Gap

Generalized Gap

Transfer Rate

Key Findings

Two-part and generalized epiplexity are highly correlated (r > 0.999) across all sequence lengths
Complement and reversal invariance transfers exactly between formulations
XOR-shift separations are amplified ~2x under the generalized measure
Generalized measure shows stronger content discrimination at all time budgets

Separation Under Transforms

Transform:

Factorization Dependence

Measure:

Structural vs. Random Content

Measure:

Convergence & Correlation