First-Order Logic with Reachability Predicates on Infinite Systems

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First-Order Logic with Reachability Predicates on Infinite Systems
This paper focuses on first-order logic (FO) extended by reachability predicates such that the expressiveness and hence decidability properties lie between FO and monadic second-order logic (MSO): in FO(R) one can demand that a node is reachably from another by some sequence of edges, whereas in FO(Reg) a regular set of allowed edge sequences can be given additionally. We study FO(Reg) logic in infinite grid-like structures which are important in verification. The decidability of logics between FO and MSO on those simple structures turns out to be sensitive to various parameters. Furthermore we introduce a transformation for infinite graphs called setbased unfolding which is based on an idea of Lohrey and Ondrusch. It allows to transfer the decidability of MSO to FO(Reg) onto the class of transformed structures. Finally we extend regular ground tree rewriting with a skeleton tree. We show that graphs specified in this way coincide with those expressible by vertex replacement and produ...
Stefan Schulz
Added 11 Feb 2011
Updated 11 Feb 2011
Type Journal
Year 2010
Authors Stefan Schulz
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