关于非相容上下文无关文法的普适性和包含问题的复杂性
On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars
摘要：
研究了无二义性有限自动机和上下文无关文法的普适性和包含问题的计算复杂性。我们观察到，几个这样的问题可以减少到明确的上下文无关文法的普遍性问题。后一个问题一直被认为是可判定的，我们提出了一个PSPACE算法，其工作原理是通过减少到卷积递归方程的零问题。我们不知道任何非平凡的复杂性下限。然而，我们表明，计算明确的上下文无关语言的硬币翻转度量（普遍性的定量概括）对于长期存在的开放问题SQRTSUM来说是困难的。
英文摘要：
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous context-free grammars. The latter problem has long been known to be decidable and we propose a PSPACE algorithm that works by reduction to the zeroness problem of recurrence equations with convolution. We are not aware of any non-trivial complexity lower bounds. However, we show that computing the coin-flip measure of an unambiguous context-free language, a quantitative generalisation of universality, is hard for the long-standing open problem SQRTSUM.
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