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We study the computational complexity of universality and inclusion problemsfor unambiguous finite automata and context-free grammars. We observe thatseveral such problems can be reduced to the universality problem forunambiguous context-free grammars. The latter problem has long been known to bedecidable and we propose a PSPACE algorithm that works by reduction to thezeroness problem of recurrence equations with convolution. We are not aware ofany non-trivial complexity lower bounds. However, we show that computing thecoin-flip measure of an unambiguous context-free language, a quantitativegeneralisation of universality, is hard for the long-standing open problemSQRTSUM.

On the complexity of the universality and inclusion problems for unambiguous context-free grammars (technical report)