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A Nearly-Quadratic Gap between Adaptive and Non-adaptive Property Testers(Extended Abstract)

机译:适应性和非自适应性能测试仪之间的几乎二次差距(扩展摘要)

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We show that for all integers t > 8 and arbitrarily small> 0, there exists a graph property H (which depends on l) such that depends&testing II has non-adaptive query complexity Q = ) whereq = e(E~(-1) )is the adaptive query complexity. This resolves the questionof how beneficial adaptivity is, in the context of proximity-dependentproperties. This also gives evidence that the canonical transformation ofGoldreich and Trevisan is essentially optimal when converting an adap-tive property tester to a non-adaptive property tester. `lb do so, we provide optimal adaptive and non-adaptive testers forthe combined property of having maximum degree O(~N) and being ablow-up collection of an arbitrary base graph H.
机译:我们表明,对于所有整数T> 8和任意小> 0,存在图形属性h(这取决于l),使得依赖性和测试II具有非自适应查询复杂度q =),其中q = e(e〜(-1) )是自适应查询复杂性。这解决了在邻近依赖性的上下文中有益适应性如何有益的问题。这还提供了证据表明,在将适应性属性测试仪转换为非自适应性能测试仪时,Goldreich和Tevisan的规范转换基本上是最佳的。 `LB这样做,我们向该最佳自适应和非自适应测试仪提供最大程度的o(〜n)并逐渐收集任意基础图H.

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