article

Complexity of Decision Problems for XML Schemas and Chain Regular Expressions

Authors:

Thomas SchwentickAuthors Info & Claims

SIAM Journal on Computing, Volume 39, Issue 4

Pages 1486 - 1530

Published: 01 November 2009 Publication History

Abstract

We study the complexity of the inclusion, equivalence, and intersection problem of extended chain regular expressions (eCHAREs). These are regular expressions with a very simple structure: they basically consist of the concatenation of factors, where each factor is a disjunction of strings, possibly extended with “$*$”, “$+$”, or “$?$”. Though of a very simple form, the usage of such expressions is widespread as eCHAREs, for instance, constitute a super class of the regular expressions most frequently used in practice in schema languages for XML. In particular, we show that all our lower and upper bounds for the inclusion and equivalence problem carry over to the corresponding decision problems for extended context-free grammars, and to single-type and restrained competition tree grammars. These grammars form abstractions of document type definitions (DTDs), XML schema definitions (XSDs) and the class of one-pass preorder typeable XML Schemas, respectively. For the intersection problem, we show that obtained complexities only carry over to DTDs. In this respect, we also study two other classes of regular expressions related to XML: deterministic expressions and expressions where the number of occurrences of alphabet symbols is bounded by a constant.

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cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 39, Issue 4

September 2009

447 pages

ISSN:0097-5397

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 November 2009

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https://dl.acm.org/doi/10.1145/3517804.3526066
Martens WPopp TLibkin LBarceló P(2022)The Complexity of Regular Trail and Simple Path Queries on Undirected GraphsProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3524149(165-174)Online publication date: 12-Jun-2022
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Doleschal JKimelfeld BMartens WNahshon YNeven FSuciu DSkritek SKoch C(2019)Split-Correctness in Information ExtractionProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319684(149-163)Online publication date: 25-Jun-2019
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Mou XChen HLi Y(2019)Context-Free Grammars for Deterministic Regular Expressions with InterleavingTheoretical Aspects of Computing – ICTAC 201910.1007/978-3-030-32505-3_14(235-252)Online publication date: 31-Oct-2019
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