On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars
Abstract
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.
Keywords
Cite
@article{arxiv.2008.04667,
title = {On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars},
author = {Lorenzo Clemente},
journal= {arXiv preprint arXiv:2008.04667},
year = {2020}
}
Comments
In Proceedings VPT/HCVS 2020, arXiv:2008.02483. arXiv admin note: identical to arXiv:2006.05275 , which has an added appendix