On Promise Problems: A Survey

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The notion of promise problems was introduced and initially studied by Even, Selman and Yacobi (Inform. and Control, Vol. 61, pages 159–173, 1984). In this article we survey some of the applications that this notion has found in the twenty years that elapsed. These include the notion of “unique solutions”, the formulation of “gap problems” as capturing various approximation tasks, the identification of complete problems (especially for the class \({\cal SZK}\) ), the indication of separations between certain computational resources, and the enabling of presentations that better distill the essence of various proofs.

This survey started as a private communication, calling an expert’s attention to numerous applications of promise problems; specifically, to capturing various notions of approximation and to the study of statistical zero-knowledge. The current volume provided the immediate incentive to turn these sporadic notes into a more comprehensive survey.