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Graph Logics with Rational Relations

Authors :
Pablo Barcelo
Diego Figueira
Leonid Libkin
Source :
Logical Methods in Computer Science, Vol Volume 9, Issue 3 (2013)
Publication Year :
2013
Publisher :
Logical Methods in Computer Science e.V., 2013.

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 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-primitive-recursive 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 non-primitive-recursive 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.

Details

Language :
English
ISSN :
18605974
Volume :
ume 9, Issue 3
Database :
Directory of Open Access Journals
Journal :
Logical Methods in Computer Science
Publication Type :
Academic Journal
Accession number :
edsdoj.bea23cf62c84ff4a93b5be4e5233144
Document Type :
article
Full Text :
https://doi.org/10.2168/LMCS-9(3:1)2013