What is the Context of Impossibility Result?

In the context of blockchain technology, Impossibility Results often arise in discussions concerning consensus mechanisms, privacy solutions, and the trade-offs between different cryptographic primitives. For instance, certain theoretical results demonstrate the difficulty of achieving perfect anonymity while maintaining efficient transaction processing. Current research and development efforts are frequently aimed at finding practical workarounds or alternative approaches that circumvent these theoretical limitations.

Impossibility Result

Definition

An Impossibility Result in computer science or cryptography is a theoretical proof demonstrating that a particular problem cannot be solved or a specific task cannot be accomplished under a given set of assumptions or constraints. These results establish fundamental limitations on what is computationally feasible, guiding the design and understanding of secure systems. They are crucial for understanding the boundaries of what can be achieved within a given framework.

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∞Blockchain Resource Allocation

∞MPC-assisted Model

∞Game-Theory

Reasonable-World Assumptions Achieve Optimal Miner Revenue in Fee Mechanism Design

Introducing reasonable-world assumptions circumvents the zero-revenue impossibility result, enabling incentive-compatible transaction fee auctions.

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∞Miner Incentive

∞Transaction Fee Mechanism

∞Deterministic Auction

Deterministic Fee Mechanisms Cannot Be Collusion-Resistant and Incentive-Compatible

No deterministic transaction fee mechanism can be simultaneously user-incentive compatible, miner-incentive compatible, and collusion-resistant without being trivial.

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∞On-Chain Economics

∞Perfect Bayesian Equilibrium

∞Cryptographic Techniques

Active Block Producers Preclude Incentive-Compatible Transaction Fee Mechanisms

An impossibility proof shows no single TFM can align incentives for both users and active MEV-extracting block producers, mandating external design augmentation.

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∞Protocol Economics

∞Transaction Fee Mechanism

∞Trivial Mechanism

Impossibility Proof for Collusion-Resistant, Truthful, and Revenue-Maximizing Mechanisms

Foundational mechanism design proves no deterministic transaction fee auction can simultaneously ensure user truthfulness, miner revenue, and collusion resistance.

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∞Incentive Compatibility

∞Game-Theory

∞Fee Market

Multi-Party Computation Enables Fairer Incentive-Compatible Transaction Fee Mechanisms

Cryptography, via Multi-Party Computation among block producers, circumvents game-theoretic impossibility results to design non-trivial, incentive-compatible fee mechanisms.

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∞Random Oracle

∞Foundational Cryptography

∞Impossibility Result

Random Oracle Model Precludes Verifiable Delay Functions

This research fundamentally proves Verifiable Delay Functions cannot exist in the Random Oracle Model, challenging foundational assumptions for secure randomness in decentralized systems.

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∞Blockchain Economics

∞Transaction Fees

∞Miner Incentives

New Desideratum for Transaction Fee Mechanisms Reveals Inherent Design Trade-Offs

Introducing "off-chain influence proofness" reveals fundamental trade-offs in blockchain transaction fee mechanism design, critical for equitable value distribution.