使用二一次写的数组的程序方案及其捕获的复杂性类
Program schemes with binary write-once arrays and the complexity classes they capture
摘要：
我们研究了一类程序方案，NPSB，其中，除了基本的分配，非确定性猜测和while循环，我们可以访问数组;但这些数组是二进制一次写的【形】，因为它们被初始化为“零”，只能被设置为“一”。我们表明，除其他结果外，NPSB可以实现为一个矢量化的Lindstrom逻辑;有问题接受的程序计划的NPSB是不可定义的有界变量无穷逻辑${\cal L}^ω_{\inftyω}$ ;所有问题接受的程序计划的NPSB有一个零-一法;有序结构，NPSB捕获的复杂性类$[ L]^[{\scriptsize NP\normalsize}]$。程序模式类NPSB实际上是无限层次的程序模式类的并集。当我们稍微修改我们的程序计划的语义，我们发现，所得到的层次的类捕获的复杂性类$Σ^p_i$（其中$i\geq 1$）的多项式层次PH。最后，我们给出逻辑等价的复杂性理论问题“NP等于PSPACE？其中所涉及的逻辑（和程序方案的类）只定义了具有0 - 1定律的问题（因此不定义一些计算上微不足道的问题）。
英文摘要：
We study a class of program schemes, NPSB, in which, aside from basic assignments, non-deterministic guessing and while loops, we have access to arrays; but where these arrays are binary write-once in that they are initialized to `zero' and can only ever be set to `one'. We show, amongst other results, that: NPSB can be realized as a vectorized Lindstrom logic; there are problems accepted by program schemes of NPSB that are not definable in the bounded-variable infinitary logic ${\cal L}^ω_{\inftyω}$; all problems accepted by the program schemes of NPSB have a zero-one law; and on ordered structures, NPSB captures the complexity class $[ L]^[{\scriptsize NP\normalsize}]$. The class of program schemes NPSB is actually the union of an infinite hierarchy of classes of program schemes. When we amend the semantics of our program schemes slightly, we find that the classes of the resulting hierarchy capture the complexity classes $Σ^p_i$ (where $i\geq 1$) of the Polynomial Hierarchy PH. Finally, we give logical equivalences of the complexity-theoretic question `Does NP equal PSPACE?' where the logics (and classes of program schemes) involved define only problems with zero-one laws (and so do not define some computationally trivial problems).
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