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arXiv · 1501.04245

Complexity of Problems of Commutative Grammars

Eryk Kopczynski
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Abstract

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an assumption that the terminal alphabet is fixed, the membership problem for regular grammars (given v in binary and a regular commutative grammar G, does G generate v?) is P, and that the equivalence problem for context free grammars (do G_1 and G_2 generate the same language?) is in $\mathrm{Π_2^P}$.

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Eryk Kopczynski. 2015-03-23. Complexity of Problems of Commutative Grammars. https://doi.org/10.2168/lmcs-11(1%3A9)2015

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