A Techniques Oriented Survey of Bounded Queries

Abstract

One paradigm in computational complexity theory is the classification of recursive functions according to their difficulty. Time is the most common complexity measure for recursive functions. For nonrecursive functions, time is not an appropriate measure. In 1985 Richard Beigel [1] and William Gasarch [14] independently hit on the idea of measuring the complexity of a nonrecursive function f by how many queries to some set X are required to compute f . (Louise Hay had similar ideas but not quite in that form [15].) There have since been many papers in the area and an upcoming book [13]. In the book and in a prior survey [12] the main theme has been the classification of functions: given a function, how complex is it, in this measure. In this survey we instead look at the techniques used to answer such questions. Hence each section of this paper focuses on a technique. All of the results in this paper have appeared elsewhere except those in Section 8. For this reason we give sketches rather than proofs, except in Section 8. ∗Dept. of C.S. and Inst. for Adv. Comp. Stud., University of MD., College Park, MD 20742, U.S.A. (Email: gasarch@cs.umd.edu.)