[Paper Review] Nonlinear Blockchain Scalability: a Game-Theoretic Perspective

Lin Chen, Lei Xu+4 more|arXiv (Cornell University)|Jan 22, 2020

Blockchain Technology Applications and Security20 references4 citations

TL;DR

This paper presents a game-theoretic framework analyzing non-linear blockchain (NLB) systems, proving that no system can simultaneously achieve full verification, high scalability, and low finality-duration. It establishes a trade-off between scalability and finality-duration, showing that with sufficient verification depth, full verification and scalability can be achieved in NLB systems like IOTA and Graphcoin.

ABSTRACT

Recent advances in the blockchain research have been made in two important directions. One is refined resilience analysis utilizing game theory to study the consequences of selfish behaviors of users (miners), and the other is the extension from a linear (chain) structure to a non-linear (graphical) structure for performance improvements, such as IOTA and Graphcoin. The first question that comes to people's minds is what improvements that a blockchain system would see by leveraging these new advances. In this paper, we consider three major metrics for a blockchain system: full verification, scalability, and finality-duration. We { establish a formal framework and} prove that no blockchain system can achieve full verification, high scalability, and low finality-duration simultaneously. We observe that classical blockchain systems like Bitcoin achieves full verification and low finality-duration, Harmony and Ethereum 2.0 achieve low finality-duration and high scalability. As a complementary, we design a non-linear blockchain system that achieves full verification and scalability. We also establish, for the first time, the trade-off between scalability and finality-duration.

Motivation & Objective

• To analyze the fundamental trade-offs between verification, scalability, and finality-duration in non-linear blockchain (NLB) systems.
• To determine whether it is possible to simultaneously achieve high scalability, full verification, and low finality-duration in blockchain systems.
• To formalize and prove an impossibility result: no blockchain system can achieve α-partial verification for any fixed α, high scalability, and low finality-duration simultaneously.
• To design and analyze a non-linear blockchain (NLB) system that achieves both full verification and high scalability, overcoming limitations of sharding-based systems.
• To quantify the trade-off between scalability and finality-duration in NLB systems using probabilistic analysis of block propagation and verification depth.

Proposed method

• Formalizing three core blockchain properties: α-partial verification (fraction of nodes verifying a transaction), scalability (throughput proportional to number of nodes), and finality-duration (time to reach consensus).
• Modeling block propagation and verification in NLB as a random walk process, where the length of the longest chain (|L_t|) is bounded with high probability.
• Using Lemma 6 on asymmetric random walks to prove that |L_t| ≤ 5s with probability at least 1−O(ε), where s is a system parameter related to block creation rate and network delay.
• Defining verification depth ℓ ≥ O(s log s) to ensure that any transaction at time t is verified by all nodes after ℓ time units with high probability.
• Analyzing the expected growth of verified descendants of a transaction using conditional probability and expectation over block references.
• Deriving a trade-off between scalability (driven by Δ, the number of concurrent transaction processing units) and finality-duration (O(s log s)), where s = min{c₁m/Δ, c₂n}.

Experimental results

Research questions

• RQ1 Can a blockchain system simultaneously achieve high scalability, full verification (α=1), and low finality-duration?
• RQ2 What is the fundamental trade-off between scalability and finality-duration in non-linear blockchain systems?
• RQ3 Can a non-linear blockchain structure enable full verification while maintaining high scalability, unlike sharding-based systems?
• RQ4 How can verification depth be set to ensure that all nodes eventually verify a given transaction with high probability?
• RQ5 What probabilistic bounds can be established on the growth of verified block chains in a DAG-based blockchain system?

Key findings

• No blockchain system can simultaneously achieve α-partial verification for any fixed α, high scalability, and low finality-duration.
• The system achieves full verification (α=1) and high scalability in non-linear blockchains like IOTA and Graphcoin by allowing multiple blocks to be appended simultaneously in a DAG structure.
• With verification depth ℓ ≥ O(s log s), any transaction is verified by all nodes with probability at least 1−O(ε), ensuring resilience under standard assumptions.
• Finality-duration scales as O(s log s), where s = min{c₁m/Δ, c₂n}, establishing a direct trade-off between scalability (increasing Δ) and finality-duration.
• The analysis proves that |L_t| ≤ 5s for all t ≥ 0 with probability at least 1−O(ε), bounding the longest chain and enabling probabilistic verification guarantees.
• The model shows that even with partial verification, full verification can be achieved over time via probabilistic propagation in a DAG, avoiding the need for full replication.