Generalized framework for Group Testing: Queries, feedbacks and adversaries

In the Group Testing problem, objective is to learn a subset K of some much larger domain N , using shortest-possible sequence queries Q . A feedback query provides information about intersection between and Several specific feedbacks have been studied in literature, often proving different formulas for estimate complexity defined as shortest length queries' solving problem with feedback. this paper we study what are properties that influence their measurable impact. We propose generic framework covers vast majority relevant settings considered which depends on two fundamental parameters feedback: input capacity α output expressiveness β They upper bound logarithm size function image, respectively. To justify value framework, prove bounds non-adaptive, deterministic under “efficient” feedbacks, minimum, maximum general expressiveness, complement them lower all given Our also hold if could get an twisted by malicious adversary, case hidden set bigger than show slight change may result substantial worsening complexity. Additionally, analyze explicitly constructed randomized counterparts results. results provide insights most useful bits output-restricted provide, open number challenging research directions.