Pattern matching of compressed terms and contexts and polynomial rewriting

A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as
A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(ncjVar(s)j), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t0 by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l; r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XML-data bases.
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Metadaten
Author:Manfred Schmidt-Schauß
URN:urn:nbn:de:hebis:30-115440
URL:http://www.ki.informatik.uni-frankfurt.de/papers/schauss/frank-43.pdf
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (43)
Publisher:Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
Place of publication:Frankfurt [am Main]
Document Type:Working Paper
Language:English
Date of Publication (online):2011/09/19
Year of first Publication:2011
Publishing Institution:Univ.-Bibliothek Frankfurt am Main
Release Date:2011/09/19
HeBIS PPN:277090105
Institutes:Informatik
Dewey Decimal Classification:004 Datenverarbeitung; Informatik
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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