Issue Theoret. Informatics Appl. Volume 39, Number 2, April-June 2005 Page(s) 391 - 401 DOI 10.1051/ita:2005024

Theoret. Informatics Appl. 39, 391-401 (2005)
DOI: 10.1051/ita:2005024

Complexity results for prefix grammars

Markus Lohrey and Holger Petersen

University of Stuttgart, FMI, Universitätsstr. 38, 70569 Stuttgart, Germany; lohrey@informatik.uni-stuttgart.de; petersen@informatik.uni-stuttgart.de

(Received February 5, 2004. Accepted July 5, 2004.)

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

Mathematics Subject Classification. 03D03, 68Q17, 68Q42, 68Q45

Key words: Rewriting systems -- regular languages -- computational complexity


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