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.

中文翻译：

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关于无歧义上下文无关语法的普遍性和包含问题的复杂性

我们研究了无歧义有限自动机和上下文无关文法的普遍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简化为无歧义的上下文无关文法的普遍性问题。众所周知，后一个问题是可判定的，我们提出了一种 PSPACE 算法，该算法通过归约到带卷积的递推方程的零性问题来工作。我们不知道任何非平凡的复杂性下界。然而，我们表明，对于长期存在的开放问题 SQRTSUM，计算一种明确的上下文无关语言的投币度量，即普遍性的定量概括，是很困难的。