Satisfiability and containment problem of structural recursions with conditions

Abstract

Structural recursion is a general graph traversing and restructuring operation. In [9][10] we extended structural recursions with not-isempty conditions and a limited form of registers in order to simulate a large fragment of XPath 1.0 and XSLT 1.0. In this paper we address the satisfiability and containment problem of structural recursions with not-isempty conditions. We examine two cases, when else-branches are allowed in the conditions and when they are not. In the second case it turns out that the satisfiability problem can be solved in quadratic time, while the question of containment is coNP-complete in general. In the first case both problems are PSPACE-complete in general. Our results have their theoretical importance of their own, however, we hope that they can also be used to fill in some of the gaps in the research of XPath and XSLT. © 2010 Springer-Verlag.