P-selective sets, and reducing search to decision vs. self-reducibility

Several results that distinguish self-reducibility of a language L with the question of whether search reduces to decision for L are obtained. It is proved that if NE intersection co-NE not=E, then there exists a set L in NP-P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L, and L is not self-reducible. Results that distinguish adaptively randomly self-reducible sets from nonadaptively randomly self-reducible sets, results concerning tradeoffs in multipower interactive proof systems, and results that distinguish checkable languages from those that are nonadaptively checkable are obtained. Many of the results depend on new techniques for constructing P-selective sets.<>