Abstract
Polyhedral analysis infers invariant linear equalities and inequalities of imperative programs. However, the exponential complexity of polyhedral operations such as image computation and convex hull limits the applicability of polyhedral analysis. Weakly relational domains such as intervals and octagons address the scalability issue by considering polyhedra whose constraints are drawn from a restricted, user-specified class. On the other hand, these domains rely solely on candidate expressions provided by the user. Therefore, they often fail to produce strong invariants.
We propose a polynomial time approach to strongly relational analysis. We provide efficient implementations of join and post condition operations, achieving a trade off between performance and accuracy. We have implemented a strongly relational polyhedral analyzer for a subset of the C language. Initial experimental results on benchmark examples are encouraging.
This research was supported in part by NSF grants CCR-01-21403, CCR-02-20134, CCR-02-09237, CNS-0411363 and CCF-0430102, by ARO grant DAAD 19-01-1-0723 and by NAVY/ONR contract N00014-03-1-0939 and the Office of Naval Research.
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Sankaranarayanan, S., Colón, M.A., Sipma, H., Manna, Z. (2005). Efficient Strongly Relational Polyhedral Analysis. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_8
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DOI: https://doi.org/10.1007/11609773_8
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