Recognition problems and communication complexity

Abstract

A special case of combinatorial search, the recognition problem is examined in this article. (H, A,f) is a recognition problem if H is a set, A is a set system on H and f : H→{0,1} is a function. Someone chooses an arbitrary x∈ H and instead of determining x itself (which is the case in most of the search problems) we only have to determine the value f( x) for the given function f from as few questions of type “is x∈ A?” as possible, where A∈ A . The smallest number of questions needed in the worst case is called the recognition complexity of f over A on H. After surveying some general results, a new class of set systems is introduced and analyzed, generalizing Yao's model of two-party communication complexity.