Homomorphism Resolving of XPath Trees Based on Automata

As a query language for navigating XML trees and selecting a set of element nodes, XPath is ubiquitous in XML applications. One important issue of XPath queries is containment checking, which is known as a co-NP complete. The homomorphism relationship between two XPath trees, which is a PTIME problem, is a sufficient but not necessary condition for the containment relationship. We propose a new tree structure to depict XPath based on the level of the tree node and adopt a method of sharing the prefixes of multi-trees to construct incrementally the most effective automata, named XTHC (XPath Trees Homomorphism Checker). XTHC takes an XPath tree and produces the result of checking homomorphism relationship between an arbitrary tree in multi-trees and the input tree, thereinto the input tree is transformed into events which force the automata to run. Moreover, we consider and narrow the discrepancy between homomorphism relationship and containment relationship as possible as we can.