Probabilistic Analysis and Empirical Validation of Patricia Tries in Ethereum State Management

TL;DR

This paper provides a probabilistic model and empirical validation of Patricia tries in Ethereum, showing their logarithmic scaling and distribution properties, which are crucial for understanding and optimizing blockchain state management.

Contribution

It introduces a new probabilistic model for Patricia tries in Ethereum and validates it through extensive experiments, offering insights into their structure and scalability.

Findings

Average path length scales logarithmically with number of addresses

Model predictions closely match experimental results, with minimal discrepancies

Path length distribution is right-skewed, affecting worst-case scenarios

Abstract

This study presents a comprehensive theoretical and empirical analysis of Patricia tries, the fundamental data structure underlying Ethereum's state management system. We develop a probabilistic model characterizing the distribution of path lengths in Patricia tries containing random Ethereum addresses and validate this model through extensive computational experiments. Our findings reveal the logarithmic scaling of average path lengths with respect to the number of addresses, confirming a crucial property for Ethereum's scalability. The study demonstrates high precision in predicting average path lengths, with discrepancies between theoretical and experimental results not exceeding 0.01 across tested scales from 100 to 100,000 addresses. We identify and verify the right-skewed nature of path length distributions, providing insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model's accuracy. The research offers structural insights into node concentration at specific trie levels, suggesting avenues for optimizing storage and retrieval mechanisms. These findings contribute to a deeper understanding of Ethereum's fundamental data structures and provide a solid foundation for future optimizations. The study concludes by outlining potential directions for future research, including investigations into extreme-scale behavior, dynamic trie performance, and the applicability of the model to non-uniform address distributions and other blockchain systems.