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Abstract / Description of output
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 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 nonprimitiverecursive 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 nonprimitiverecursive 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 

Article number  1 
Number of pages  44 
Journal  Logical Methods in Computer Science 
Volume  9 
Issue number  3 
DOIs  
Publication status  Published  2013 
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Dive into the research topics of 'Graph Logics with Rational Relations'. 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