Width-bounded reducibility and binary search over complexity classes

A notion of width-bounded reducibility is introduced. Width-bounded reducibility provides a circuit-based realization of Ruzzo-Simon-Tompa reducibility and allows that notion of reducibility to be generalized. It is shown that reductions of simultaneously restricted width and depth provide a characterization of binary search over complexity classes, as introduced by K. Wagner (1989) and S. Buss and L. Hay (1988). This allows the presentation of a circuit-based characterization of P^NP[log]. Other results are presented that explore relationships among complexity classes, using width-bounded reductions as a tool