Dyson-Schwinger equations in the theory of computation

2013/02/20 by Colleen Delaney, Matilde Marcolli, Delaney, Colleen +1
Computer Science · Mathematics · #16T05 #18D50 #68Q30 #81T15 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Computability, Logic, AI Algorithms #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1302.5040

openalex publication_date 2013/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of algorithms computing primitive and partial recursive functions and in the halting problem.

Citations

• Renormalization and computation I: motivation and background
• Zipf's law and L. Levin's probability distributions

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• General Dyson-Schwinger equations and systems
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• A Primer on Functional Methods and the Schwinger-Dyson Equations