In the reliable transmission problem, a sender, Alice, wishes to transmit a bit-string x to a remote receiver, Bob, over a binary channel with adversarial noise. The solution to this problem is to encode x using an error correcting code. As it is long known that the distance of binary ... more >>>

Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erdos-Rado sunflower lemma. Implicit versions of the corresponding total search problems are known to be PWPP-hard; here "implicit" means that the collection is represented ... more >>>

We show that a decidable promise problem has a non-interactive statistical zero-knowledge proof system if and only if it is randomly reducible to a promise problem for Kolmogorov-random strings, with a superlogarithmic additive approximation term. This extends recent work by Saks and Santhanam (CCC 2022). We build on this to ... more >>>