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In computer science, a property testing algorithm for a decision problem is an algorithm whose query complexity to its input is much smaller than the instance size of the problem. Typically property testing algorithms are used to decide if some mathematical object (such as a graph or a boolean function) has a "global" property, or is "far" from having this property, using only a small number of "local" queries to the object. For example, the following promise problem admits an algorithm whose query complexity is independent of the instance size (for an arbitrary constant ε > 0): :"Given a graph ''G'' on ''n'' vertices, decide if ''G'' is bipartite, or ''G'' cannot be made bipartite even after removing an arbitrary subset of at most edges of ''G''." Property testing algorithms are important in the theory of probabilistically checkable proofs. ==Definition and variants== Formally, a property testing algorithm with query complexity ''q''(''n'') and ''proximity parameter'' ε for a decision problem ''L'' is a randomized algorithm that, on input ''x'' (an instance of ''L'') makes at most ''q''(|''x''|) queries to ''x'' and behaves as follows: * If ''x'' is in ''L'', the algorithm accepts ''x'' with probability at least ⅔. * If ''x'' is ε-far from ''L'', the algorithm rejects ''x'' with probability at least ⅔. Here, "''x'' is ε-far from ''L''" means that the Hamming distance between ''x'' and any string in ''L'' is at least ε|''x''|. A property testing algorithm is said to have ''one-sided error'' if it satisfies the stronger condition that the accepting probability for instances ''x ∈ L'' is 1 instead of ⅔. A property testing algorithm is said be ''non-adaptive'' if it performs all its queries before it "observes" any answers to previous queries. Such an algorithm can be viewed as operating in the following manner. First the algorithm receives its input. Before looking at the input, using its internal randomness, the algorithm decides which symbols of the input are to be queried. Next, the algorithm observes these symbols. Finally, without making any additional queries (but possibly using its randomness), the algorithm decides whether to accept or reject the input. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「property testing」の詳細全文を読む スポンサード リンク
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