XPath Query Satisfiability and Containment under DTD Constraints

In this thesis, we consider the XML query language XPath, along with XML documents whose integrity constraints are presented in the form of document type definitions (DTDs). In particular, we study the problems of XPath satisfiability and XPath containment in the presence of DTDs. The motivation for studying XPath is that it is the main language for navigating in and extracting information from XML documents. The motivation for studying DTDs, as opposed to some other newer XML schema formalism, is that DTDs are well-known, stable, and well-tested. Furthermore, they are still widely-used in various domains. The major contributions of the thesis can be classified into those on satisfiability and those on containment of XPath queries under DTDs. With respect to the satisfiability problem, we show that the XPath satisfiability problem for the fragment XP{/,[ ]} is NPhard in general. In order to study whether this worst-case behaviour arises often in practice, we investigate real-world DTDs and discover that the majority of them satisfy a property we called the covering property. We then show that XPath satisfiability for the fragment XP{/,[ ],∗,//,∪} is in PTIME under covering DTDs. We also show that it is decidable in PTIME for duplicate-free DTDs (a property introduced in [91]), which also occur often in practice. Despite the positive results for the satisfiability problem, we prove that XPath containment under covering DTDs for XP{/,[ ]} is still coNP-hard. However, we define a class of DTDs, called well-behaved DTDs, under which containment for XP{/,[ ]} is tractable