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On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars
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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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Cited by 1 Pith paper
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On the Complexity of Language Membership for Probabilistic Words
Probabilistic membership for context-free languages is in PTIME for unambiguous and poly-slicewise-unambiguous languages, #P-hard for some unions of two linear unambiguous CFLs, and tractable via complement-capable ci...
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