Abstract
We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The number and dimensionality of the LP queries are polynomial in the program dimensionality, size and the number of target invariants. The method generalizes similar analyses in the interval, octagon, and octahedra domains, without resorting to polyhedral manipulations. We demonstrate the performance of our method on some benchmark programs.
This research was supported in part by NSF grants CCR-01-21403, CCR-02-20134 and CCR-02-09237, by ARO grant DAAD19-01-1-0723, by ARPA/AF contracts F33615-00-C-1693 and F33615-99-C-3014, by NAVY/ONR contract N00014-03-1-0939, and by the Siebel Graduate Fellowship.
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Sankaranarayanan, S., Sipma, H.B., Manna, Z. (2005). Scalable Analysis of Linear Systems Using Mathematical Programming. In: Cousot, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30579-8_2
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DOI: https://doi.org/10.1007/978-3-540-30579-8_2
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