Background on Computation Complexity Metrics

The blog post, part of a Chainlink Labs Research Team series on zero-knowledge (ZK) proofs, explores the complexity of computational circuits, emphasizing their significance in designing scalable ZK protocols. It compares circuits and Turing machines, highlighting circuits' simplicity and their limitation to bounded computation, unlike Turing machines' ability to run indefinitely. The post delves into computational complexity metrics, particularly representation and runtime space complexities, noting that uniformity in computation can reduce resource requirements. It uses examples, such as a basic circuit and an ℓ-bit adder, to illustrate how uniformity leads to better runtime space complexity by allowing the reuse of computation patterns. The discussion extends to how these complexities impact ZK protocols, particularly noting that interactive ZK proofs can benefit from the ability to discard unnecessary values, unlike succinct ZK proofs, which typically require memory linear to the number of gates. The post suggests that interactive proofs using the commit-and-prove paradigm offer more memory-efficient approaches in ZK protocol applications.

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