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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 nonmultiplyrecursive complexity (e.g., for subsequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has nonmultiplyrecursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.
Original language  English 

Title of host publication  Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science, LICS 2012 
Publisher  Institute of Electrical and Electronics Engineers (IEEE) 
Pages  115124 
Number of pages  10 
ISBN (Print)  9781467322638 
DOIs  
Publication status  Published  2012 
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Dive into the research topics of 'Graph Logics with Rational Relations and the Generalized Intersection Problem'. Together they form a unique fingerprint.Projects
 2 Finished


XML with Incomplete Information: Representation, Querying and Applications
1/09/09 → 30/11/13
Project: Research