Extracting Minimum Length Document Type Definitions Is NP-Hard

Abstract

XML (eXtensible Markup Language) is becoming more and more popular. Since not all XML documents come with a (proper) accompanying Document Type Descriptors (DTD), it is a challenge to find “good” DTDs automatically. Note that many optimization procedures rely on being given a well-fitting DTD to work properly.

M. Garofalakis et al. have developed XTRACT, a system for extracting Document Type Descriptors (DTD) from XML documents. This system may actually integrate many of the other proposals as kind of subroutines, since it finally tries to find the “best” DTD out of those proposals. Due to the connections to regular expression (inference), see [1,2], any good inference algorithm for regular expressions can hence be incorporated. Observe that the regular expressions which are generated by first using learning algorithms designed for deterministic finite automata and then turning these automata into regular expressions by “textbook algorithms” (as proposed in [2]) tend to produce expressions which are rather “unreadable” from a human perspective. In the envisaged application – the extraction of DTDs – this is particularly bad, since those DTDs are meant to be read and understood by humans. This is one of the reasons why the Grammatical Inference community should get interested in MDL approaches to learning as proposed with the XTRACT project.