New Bounds for the Language Compression Problem
نویسندگان
چکیده
The CD complexity of a stringx is the length of the shortest polynomial time program which accepts only the string x. The language compression problem consists of giving an upper bound on the CDA n complexity of all strings x in some set A. The best known upper bound for this problem is 2 log(jjA njj) + O(log(n)), due to Buhrman and Fortnow. We show that the constant factor 2 in this bound is optimal. We also give new bounds for a certain kind of random sets R f0; 1gn, for which we show an upper bound of log(jjR njj) + O(log(n)).
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