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• W2908766690 abstract "We present $${textsc {Dryad}}_textit{dec}$$ , a decidable logic that allows reasoning about tree data-structures with measurements. This logic supports user-defined recursive measure functions based on Max or Sum, and recursive predicates based on these measure functions, such as AVL trees or red-black trees. We prove that the logic’s satisfiability is decidable. The crux of the decidability proof is a small model property which allows us to reduce the satisfiability of $${textsc {Dryad}}_textit{dec}$$ to quantifier-free linear arithmetic theory which can be solved efficiently using SMT solvers. We also show that $${textsc {Dryad}}_textit{dec}$$ can encode a variety of verification and synthesis problems, including natural proof verification conditions for functional correctness of recursive tree-manipulating programs, legality conditions for fusing tree traversals, synthesis conditions for conditional linear-integer arithmetic functions. We developed the decision procedure and successfully solved 220+ $${textsc {Dryad}}_textit{dec}$$ formulae raised from these application scenarios, including verifying functional correctness of programs manipulating AVL trees, red-black trees and treaps, checking the fusibility of height-based mutually recursive tree traversals, and counterexample-guided synthesis from linear integer arithmetic specifications. To our knowledge, $${textsc {Dryad}}_textit{dec}$$ is the first decidable logic that can solve such a wide variety of problems requiring flexible combination of measure-related, data-related and shape-related properties for trees." @default.
• W2908766690 created "2019-01-25" @default.
• W2908766690 creator A5041566154 @default.
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• W2908766690 date "2019-01-01" @default.
• W2908766690 modified "2023-09-26" @default.
• W2908766690 title "A Decidable Logic for Tree Data-Structures with Measurements" @default.
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• W2908766690 doi "https://doi.org/10.1007/978-3-030-11245-5_15" @default.
• W2908766690 hasPublicationYear "2019" @default.
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