## Kopczynski, Eryk - Complexity of Problems of Commutative Grammars

lmcs:875 - Logical Methods in Computer Science, March 25, 2015, Volume 11, Issue 1
Complexity of Problems of Commutative Grammars

Authors: Kopczynski, Eryk

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 $\mathrm{\Pi_2^P}$.

Source : oai:arXiv.org:1501.04245
DOI : 10.2168/LMCS-11(1:9)2015
Volume: Volume 11, Issue 1
Published on: March 25, 2015
Submitted on: January 9, 2014
Keywords: Computer Science - Formal Languages and Automata Theory