Fig. 1. An XML Schema definition bib.xsd.

Fig. 2. Example XML document conforming to the XML Schema definition of Fig. 1.

Fig. 3. A data model of the XML Schema language for evaluating XPath queries on XML Schema definitions.

Fig. 4. Example XPath query Q and its sub-expressions.

Fig. 5. Schema paths of query Q.

Fig. 6. Graphical representation of the schema paths of Fig. 5, where we only present the last node of the node sequences of the records of the schema paths.

Fig. 7. The function L: XPath x schema_path x XPath → Set(schema_path) is defined recursively on the structure of XPath expressions.

Fig. 8. The function L: XPath x schema_path x XPath → Set(schema_path) for evaluating axis and node test.

Fig. 9. The function L: XPath x schema_path x XPath → Set(schema_path) for evaluating predicates.

Fig. 10. The function L: XPath x schema_path x XPath → Set(schema_path) for integrating data type checking.

Fig. 11. The function L: XPath x schema_path x XPath → Set(schema_path) for integrating occurrence constraints checking.

Fig. 12. The function L: XPath x schema_path x XPath → Set(schema_path) for integrating fixed value checking.

Fig. 13. Filtering Q1--Q11 by our approach.

Fig. 14. Evaluating Q1--Q11 using the Saxon evaluator.

Fig. 15. Evaluating Q1--Q11 using the Qizx evaluator.

Fig. 16. Speedup by our approach over Saxon when evaluating Q1--Q11.

Fig. 17. Speedup by our approach over Qizx when evaluating Q1--Q11.

Fig. 18. Filtering Q12--Q26 by our approach.

Fig. 19. Evaluating Q12--Q26 using the Saxon evaluator.

Fig. 20. Evaluating Q12--Q26 using the Qizx evaluator.

Fig. 21. Speedup by our approach over Saxon when evaluating Q12--Q26.

Fig. 22. Speedup by our approach over Qizx when evaluating Q12--Q26.

Fig. 23. Time of evaluating unsatisfiable queries (Q1--Q11) and satisfiable queries (Q1–Q11) by our evaluator.

Fig. 24. Time of evaluating unsatisfiable queries (Q12--Q26) and satisfiable queries (Q12–Q26) by our evaluator.

Fig. 25. Evaluation of queries Q1–Q11 using Saxon.

Fig. 26. Evaluation of queries Q1–Q11 using Qizx.

Fig. 27. Ratio of the time used by our approach over the time used by Saxon when evaluating Q1–Q11.

Fig. 28. Ratio of the time used by our approach over the time used by Qizx when evaluating Q1–Q11.

Queries with incorrect semantics or structure

Queries with correct semantics and structure

Queries not conforming to data-types or occurrence constraints

Queries conforming to data-types and occurrence constraints