查询-单调图灵约简
Query-Monotonic Turing Reductions
摘要：
我们研究减少，限制图灵减少的极端适应性。特别是，我们研究的减少，使一个快速的，结构化的进展，通过他们减少的集合：每个查询严格比前一个更长（更短）。我们称这些约简为查询增加（查询减少）图灵约简。我们还研究查询非增加（查询非减少）图灵约简。这些是图灵约简，其中查询长度的序列是非递增（非递减）的。我们要问，这些限制是否实际上限制了还原的力量。我们证明了查询增加和查询减少图灵约简与真值表约简是不可比较的（即，既不严格强于也不严格弱于），并且严格弱于图灵约简。此外，我们证明了查询非增和查询非减图灵约简严格强于真值表约简，严格弱于图灵约简。尽管事实上，我们证明了查询增加和查询减少图灵约简在一般情况下严格弱于图灵约简，我们确定了一个广泛的集合A类，其中任何图灵约简到A的集合也将通过查询增加和查询减少图灵约简到A。特别地，这适用于所有紧可填充集合，其中如果集合是经由其输出长度从输入的长度的上方和下方两者紧密地界定的函数可填充的，则集合被称为紧可填充的。我们证明了许多自然的NP完全问题，如可满足性，团，顶点覆盖是紧paddable。
英文摘要：
We study reductions that limit the extreme adaptivity of Turing reductions. In particular, we study reductions that make a rapid, structured progression through the set to which they are reducing: Each query is strictly longer (shorter) than the previous one. We call these reductions query-increasing (query-decreasing) Turing reductions. We also study query-nonincreasing (query-nondecreasing) Turing reductions. These are Turing reductions in which the sequence of query lengths is nonincreasing (nondecreasing). We ask whether these restrictions in fact limit the power of reductions. We prove that query-increasing and query-decreasing Turing reductions are incomparable with (that is, are neither strictly stronger than nor strictly weaker than) truth-table reductions and are strictly weaker than Turing reductions. In addition, we prove that query-nonincreasing and query-nondecreasing Turing reductions are strictly stronger than truth-table reductions and strictly weaker than Turing reductions. Despite the fact that we prove query-increasing and query-decreasing Turing reductions to in the general case be strictly weaker than Turing reductions, we identify a broad class of sets A for which any set that Turing reduces to A will also reduce to A via both query-increasing and query-decreasing Turing reductions. In particular, this holds for all tight paddable sets, where a set is said to be tight paddable exactly if it is paddable via a function whose output length is bounded tightly both from above and from below in the length of the input. We prove that many natural NP-complete problems such as satisfiability, clique, and vertex cover are tight paddable.
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