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Complexity results for prefix grammars

Published online by Cambridge University Press:  15 April 2005

Markus Lohrey  and
Holger Petersen
Markus Lohrey
Affiliation:
University of Stuttgart, FMI, Universitätsstr. 38, 70569 Stuttgart, Germany; lohrey@informatik.uni-stuttgart.de; petersen@informatik.uni-stuttgart.de
Holger Petersen
Affiliation:
University of Stuttgart, FMI, Universitätsstr. 38, 70569 Stuttgart, Germany; lohrey@informatik.uni-stuttgart.de; petersen@informatik.uni-stuttgart.de
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Abstract

Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE. We also showthat membership for these grammars is complete in P (it was known that this problem is in P) and characterize thecomplexity of equivalence and inclusion for monotonic grammars. For grammars with several premises we show that membershipis complete in EXPTIME and hard for PSPACE for monotonicgrammars.

Keywords

Rewriting systemsregular languagescomputational complexity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 2 , April 2005 , pp. 391 - 401
Copyright
© EDP Sciences, 2005

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