Graph Logics with Rational Relations and the Generalized Intersection Problem

Abstract—We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword (factor) or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with non-multiply-r...

• Type: Journal
• Year: 2012
• Where: LICS
• Authors: Pablo Barceló, Diego Figueira, Leonid Libkin
• Keywords: Automated Reasoning, Graph Topology, LICS 2012, Nonempty Intersection, Rational Relations