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Higher-Order Nonemptiness Step by Step
[article]

2020
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arXiv
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pre-print

We show a new simple algorithm that checks whether a given higher-order grammar generates a nonempty language of trees. The algorithm amounts to a procedure that transforms a grammar of order n to a grammar of order n-1, preserving nonemptiness, and increasing the size only exponentially. After repeating the procedure n times, we obtain a grammar of order 0, whose nonemptiness can be easily checked. Since the size grows exponentially at each step, the overall complexity is n-EXPTIME, which is

arXiv:2009.08174v1
fatcat:6tul6byghnbkfo45swdkmitaue