City Research Online

Two variables per linear inequality as an abstract domain

Simon, A., King, A. & Howe, J. M. (2003). Two variables per linear inequality as an abstract domain. Logic based program synthesis and transformation, 2664, pp. 71-89. doi: 10.1007/3-540-45013-0_7

Abstract

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.

Publication Type: Article
Additional Information: The original publication is available at www.springerlink.com
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science
[thumbnail of Two_variables_per_linear_inequality_as_an_abstract_domain.pdf]
Preview
PDF
Download (284kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login