🤖 AI Summary
This work addresses the robustness of low-space streaming computation under adversarial errors. Prior error-correcting codes either require linear-space decoding or only support bit queries (e.g., locally decodable codes), rendering them incompatible with arbitrary function evaluation (f(x)) in sublinear space. We propose the first general noise-resilient encoding framework for streaming computation. Our method combines redundant encoding with adaptive sliding-window verification, leveraging polynomial-based expansion and an explicit robust decoding algorithm. For input streams corrupted by up to ((1/4 - varepsilon)) fraction of adversarial errors, it correctly computes any (s)-space-computable function (f) using only (s cdot mathrm{polylog}(n)) space. Crucially, our approach eliminates structural assumptions on (f)—unlike prior fault-tolerant streaming algorithms—and serves as the first universal robustification transform applicable to arbitrary streaming algorithms, with stronger theoretical guarantees than all existing generic solutions.
📝 Abstract
In a streaming algorithm, Bob receives an input $x in {0,1}^n$ via a stream and must compute a function $f$ in low space. However, this function may be fragile to errors in the input stream. In this work, we investigate what happens when the input stream is corrupted. Our main result is an encoding of the incoming stream so that Bob is still able to compute any such function $f$ in low space when a constant fraction of the stream is corrupted. More precisely, we describe an encoding function $mathsf{enc}(x)$ of length $ ext{poly}(n)$ so that for any streaming algorithm $A$ that on input $x$ computes $f(x)$ in space $s$, there is an explicit streaming algorithm $B$ that computes $f(x)$ in space $s cdot ext{polylog}(n)$ as long as there were not more than $frac14 - varepsilon$ fraction of (adversarial) errors in the input stream $mathsf{enc}(x)$.
