代数机器的下界，语义上
Lower bounds for algebraic machines, semantically
摘要：
提出了一种新的证明计算复杂性下界的语义方法。我们用它来证明，最大流量，PTIME完全的问题，是不计算的多对数时间的并行随机存取机（PRAMs）与整数，显示NCZ \neq PTIME，其中NCZ是复杂性类定义的机器，PTIME是标准类的多项式时间可计算的问题（上，说，一个图灵机）。在显示这个新的分离结果的顶部，我们表明我们的方法捕获以前的下界结果从文献：斯蒂尔和姚的代数决策树的下界，本-或代数计算树的下界，Cucker的证明NC不等于PTIME的实数，和Mulmuley的下界“PRAMs没有位操作”。
英文摘要：
This paper presents a new semantic method for proving lower bounds in computational complexity. We use it to prove that maxflow, a PTIME complete problem, is not computable in polylogarithmic time on parallel random access machines (PRAMs) working with integers, showing that NCZ \neq PTIME, where NCZ is the complexity class defined by such machines, and PTIME is the standard class of polynomial time computable problems (on, say, a Turing machine). On top of showing this new separation result, we show our method captures previous lower bounds results from the literature: Steele and Yao's lower bounds for algebraic decision trees, Ben-Or's lower bounds for algebraic computation trees, Cucker's proof that NC is not equal to PTIME on the reals, and Mulmuley's lower bounds for "PRAMs without bit operations".
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