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Develop efficient estimators for sophistication and effective complexity

Develop efficient methods to estimate sophistication and effective complexity of strings so they can be applied to measure structure beyond i.i.d. token statistics in the computational experiments, reducing reliance on proxy measures such as compression-based approximations.

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Background

The paper introduces “high-order entropy” as a practical complexity measure, approximating Kolmogorov complexity via compression, because rigorous measures like sophistication and effective complexity lack efficient estimators. This limitation motivates the new metric.

An efficient estimation method for sophistication or effective complexity would allow direct evaluation of structured information in strings and more robust analysis of state transitions and emergent replicators.

References

This metric shares similarities with sophistication and effective complexity, because it attempts to “factor out” information in the string that comes from sampling i.i.d. variables. Nevertheless, we are not aware of methods to efficiently estimate these metrics.

— Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction (2406.19108 - Arcas et al., 27 Jun 2024) in Section 2, Subsection “Primordial soup simulations,” paragraph “Complexity metrics”