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uh we can probably get started so um welcome everyone uh to the uh last seminar in the uh one world combinatorics onward seminar before we take a break for the summer and um we are very pleased to have uh zachary chase uh giving the uh the talk today from the university of oxford and he is going to talk about uh three related problems the separating words problem the k dec problem and the trace reconstruction problem okay um can you hear me fine yeah absolutely okay um okay thanks a lot for the invitation and yeah so today i want to talk about three related problems that i really like and for each of them theres yeah the the gaps theres an exponential gap between the upper and lower bound so much more work needs to be done so i hope this will entice some people to work on some of the problems um okay so yes three difficult questions so let x and y be appear distinct zero one strings of length n okay the first question is is there a deterministic finite autonomous on a dfa with uh at