Figure 1

Searching by counting.

A solution to a search problem instance x can be inferred from a sequence of a small number of counts. In the example shown there is a single solution S(x) = 1001 and each blue circle represents an enumeration of solutions to x of length 4 ending in suffix w′. An empty or filled circle indicates that the count returned zero or one, respectively. The red dotted line shows the path to the solution inferred from these counts. For the first count (upper most circle), w′ has zero length, i.e., all solutions of length 4 are counted and we infer there is a solution of this length. For the next count and we infer that solutions must begin with suffix 1. For the third count and we infer that there is a solution beginning with suffix 01 and so on.