In the trace reconstruction problem , an unknown source string x ∈ {0, 1} n is sent through a probabilistic deletion channel which independently deletes each bit with probability δ and concatenates surviving bits, yielding of . The to reconstruct given independent traces. This has received much attention in recent years both worst-case setting where may be arbitrary [DOS19, NP17, HHP18, HL20, C...

This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to di erent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.