Theoretical impossibility describes a concept or outcome that cannot occur under a given set of established principles or assumptions. It indicates a fundamental limit derived from logical deduction or scientific understanding. In the context of computer science and cryptography, it often refers to tasks that cannot be solved within reasonable time or resource constraints. This concept helps define the boundaries of what is achievable.
Context
In blockchain and cryptographic research, understanding theoretical impossibility is crucial for identifying the inherent limitations of distributed systems. For instance, the CAP theorem highlights a theoretical impossibility in achieving all three properties of consistency, availability, and partition tolerance simultaneously. A key discussion involves how developers navigate these fundamental constraints when designing new protocols. Future advancements often seek to approximate or circumvent these theoretical limits through innovative architectural solutions.
A new trilemma proves that efficient, adaptively secure consensus requires a logarithmic lower bound on public randomness consumption, fundamentally limiting design space.
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