Width-Bounded Reducibility and Binary Search over Complexity Classes

We introduce a notion of width-bounded reducibility. Width-bounded reducibility provides a circuit-based realization of RuzzoSimon-Tompa reducibility [RS-84], and allows us to generalize that notion of reducibility. We show that reductions of simultaneously restricted width and depth provide a characterization of binary search over complexity classes, as introduced by Wagner [Wa-89] and Buss and Hay [BH-88]. This allows us to present a circuit-based characterization of P. Other results are presented that explore relationships among complexity classes, using width-bounded reductions as a tool.