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Two Variables per Linear Inequality as an Abstract Domain

Simon, Axel and King, Andy and Howe, Jacob M. (2002) Two Variables per Linear Inequality as an Abstract Domain. In: Leuschel, Michael, ed. Logic Based Program Synthesis and Transformation 12th International Workshop. Lecture Notes in Computer Science . Springer, Berlin, Germany, pp. 71-89. ISBN 978-3-540-40438-5. E-ISBN 978-3-540-45013-9. (doi:10.1007/3-540-45013-0_7) (KAR id:13681)

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This paper explores the spatial domain of sets of inequalities where each inequality contains at most two variables - a domain that is richer than intervals and more tractable than general polyhedra. We present a complete suite of efficient domain operations for linear systems with two variables per inequality with unrestricted coefficients. We exploit a tactic in which a system of inequalities with at most two variables per inequality is decomposed into a series of projections - one for each two dimensional plane. The decomposition enables all domain operations required for abstract interpretation to be expressed in terms of the two dimensional case. The resulting operations are efficient and include a novel planar convex hull algorithm. Empirical evidence suggests that widening can be applied effectively, ensuring tractability.

Item Type: Book section
DOI/Identification number: 10.1007/3-540-45013-0_7
Additional information: see
Uncontrolled keywords: Convex Hull, Logic Program, Linear Inequality, Abstract Interpretation, Abstract Domain
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Sciences > School of Computing > Theoretical Computing Group
Depositing User: Andy King
Date Deposited: 24 Nov 2008 17:59 UTC
Last Modified: 15 Feb 2020 04:01 UTC
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