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arXiv · 1311.7442

Irreducibility is Minimum Synergy Among Parts

Virgil Griffith·Jonathan Harel
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Abstract

For readers already familiar with Partial Information Decomposition (PID), we show that PID's definition of synergy enables quantifying at least four different notions of irreducibility. First, we show four common notions of "parts" give rise to a spectrum of four distinct measures of irreducibility. Second, we introduce a nonnegative expression based on PID for each notion of irreducibility. Third, we delineate these four notions of irreducibility with exemplary binary circuits. This work will become more useful once the complexity community has converged on a palatable $\operatorname{I}_{\cap}$ or $\operatorname{I}_{\cup}$ measure.

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Virgil Griffith, Jonathan Harel. 2013-12-12. Irreducibility is Minimum Synergy Among Parts. https://arxiv.org/abs/1311.7442

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