The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.
A New Approach to Formal Language Theory by Kolmogorov Complexity
我们提出了一种新的方法来形式语言理论使用柯尔莫哥洛夫复杂性。本文的主要结果是一种泵引理的替代方法，一种正则语言的新刻画，以及一种区分确定性上下文无关语言和非确定性上下文无关语言的新方法。许多例子说明了新的“不可压缩性参数”的使用。这种方法在乔姆斯基层次结构的高端的也是成功的，因为人们可以用柯尔莫哥洛夫复杂度来量化非递归性。(This这是一个未经修正的初步版本。最终版本是发表在SIAM J. COMPUT.上的版本，24：2（1995），398-410.）
Rational Reductions and Regular Languages of Constant Circuit Complexity
School of Electrical Engineering and Computer Science, Universität Kassel（卡塞尔大学电气与计算机工程学院）；School of Mathematics and Computer Science, Indian Institute of Technology Goa（印度理工学院果阿分校数学与计算机学院）
