针对建议上下文无关语言的伪随机生成器
Pseudorandom Generators Against Advised Context-Free Languages
摘要：
伪随机性在现代密码学中起着核心作用，在计算机科学的各个领域都有理论和实际应用。从较短但真正随机的种子生成伪随机字符串的函数称为伪随机生成器。我们的生成器被设计成欺骗语言（或者等价地，布尔值函数）。特别是，我们的生成器傻瓜建议上下文无关语言，即上下文无关语言的外部信息称为建议，而且我们的生成器几乎是一对一的，拉伸$n$位种子到$n+1$位。我们明确地构造了这样一个伪随机发生器，它是由确定性图灵机使用对数空间计算的，也属于CFLMV（2）/n--CFL的2-合取闭包的函数扩展，并借助于适当的确定性建议。相比之下，我们表明，几乎没有一对一的伪随机发生器对上下文无关的语言，如果我们要求它应该由一个非确定性的下推自动机配备了一个只写输出磁带计算。我们的生成器自然地扩展了已知的伪随机生成器对建议的正则语言。我们的CFL/n-伪随机的生成器的证明是相当初级的，特别是，证明的一部分利用了一个特殊的功能的行为的不确定性下推自动机，称为交换属性，这是有趣的，在其本身的权利，概括的交换引理上下文无关的语言。
英文摘要：
Pseudorandomness has played a central role in modern cryptography, finding theoretical and practical applications to various fields of computer science. A function that generates pseudorandom strings from shorter but truly random seeds is known as a pseudorandom generator. Our generators are designed to fool languages (or equivalently, Boolean-valued functions). In particular, our generator fools advised context-free languages, namely, context-free languages assisted by external information known as advice, and moreover our generator is made almost one-to-one, stretching $n$-bit seeds to $n+1$ bits. We explicitly construct such a pseudorandom generator, which is computed by a deterministic Turing machine using logarithmic space and also belongs to CFLMV(2)/n---a functional extension of the 2-conjunctive closure of CFL with the help of appropriate deterministic advice. In contrast, we show that there is no almost one-to-one pseudorandom generator against context-free languages if we demand that it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape. Our generator naturally extends known pseudorandom generators against advised regular languages. Our proof of the CFL/n-pseudorandomness of the generator is quite elementary, and in particular, one part of the proof utilizes a special feature of the behaviors of nondeterministic pushdown automata, called a swapping property, which is interesting in its own right, generalizing the swapping lemma for context-free languages.
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