On Self-Reducible Sets of Low Information Content

Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of self-reducible sets which are \almost" in P (i.e. sets in APT 0). Self-reducible sets with low instance complexity (i.e. sets in ICClog; poly]) are shown to be in NP \ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in P NP , if they are self-reducible in a little more restricted sense of self-reducibility.