Theoretical computer science · Oct 6, 2026
Quantitative trace-reconstruction bounds with a uniform decoder
At every fixed deletion probability in , reconstructing an arbitrary length-n binary string requires independent traces, ruling out polynomial-sample reconstruction. A uniform decoder achieves quasipolynomial sample and running-time bounds for known fixed rational retention probabilities. When the deletion probability is at most for fixed ε > 0, both bounds become polynomial in the input and parameter encoding.
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