Verifying monadic second-order properties of graph programs

The core challenge in a Hoare- or Dijkstra-style proof system for graph programs is in defining a weakest liberal precondition construction with respect to a rule and a postcondition. Previous work addressing this has focused on assertion languages for first-order properties, which are unable to exp...

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Bibliographic Details
Main Authors: POSKITT, Christopher M., PLUMP, Detlef
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2014
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Online Access:https://ink.library.smu.edu.sg/sis_research/4912
https://ink.library.smu.edu.sg/context/sis_research/article/5915/viewcontent/PoskittPlump.ICGT.2014.pdf
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Institution: Singapore Management University
Language: English
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Summary:The core challenge in a Hoare- or Dijkstra-style proof system for graph programs is in defining a weakest liberal precondition construction with respect to a rule and a postcondition. Previous work addressing this has focused on assertion languages for first-order properties, which are unable to express important global properties of graphs such as acyclicity, connectedness, or existence of paths. In this paper, we extend the nested graph conditions of Habel, Pennemann, and Rensink to make them equivalently expressive to monadic second-order logic on graphs. We present a weakest liberal precondition construction for these assertions, and demonstrate its use in verifying non-local correctness specifications of graph programs in the sense of Habel et al.