有界下推维与Lempel Ziv信息密度
Bounded Pushdown dimension vs Lempel Ziv information density
摘要：
在本文中，我们介绍了一个变种的下推维数称为有界下推（BPD）维，它测量的密度包含在一个序列中的信息，相对于一个BPD自动机，即一个有限的状态机配备了一个额外的无限内存堆栈，与额外的要求，每个输入符号只允许有限数量的堆栈运动。BPD自动机是下推自动机的一种自然的实时限制。我们证明了BPD维数是一个强大的概念，通过给出一个等价的BPD维数的BPD压缩机的特征。然后，我们研究BPD压缩之间的关系，和标准的Lempel-Ziv（LZ）压缩算法，并表明，在有限状态压缩机的情况下，LZ是不是普遍的有界下推压缩机在很强的意义上：我们构建一个序列，LZ未能压缩显着，但至少由一个因子2压缩的BPD压缩机。作为推论，我们得到了一个强分离的有限状态和BPD维数。
英文摘要：
In this paper we introduce a variant of pushdown dimension called bounded pushdown (BPD) dimension, that measures the density of information contained in a sequence, relative to a BPD automata, i.e. a finite state machine equipped with an extra infinite memory stack, with the additional requirement that every input symbol only allows a bounded number of stack movements. BPD automata are a natural real-time restriction of pushdown automata. We show that BPD dimension is a robust notion by giving an equivalent characterization of BPD dimension in terms of BPD compressors. We then study the relationships between BPD compression, and the standard Lempel-Ziv (LZ) compression algorithm, and show that in contrast to the finite-state compressor case, LZ is not universal for bounded pushdown compressors in a strong sense: we construct a sequence that LZ fails to compress signicantly, but that is compressed by at least a factor 2 by a BPD compressor. As a corollary we obtain a strong separation between finite-state and BPD dimension.
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