This paper describes a precise numerical abstract domain for use in timing analysis. The numerical abstract domain is parameterized by a linear abstract domain and is constructed by means of two domain lifting operations. One domain lifting operation is based on the principle of expression abstraction (which involves defining a set of expressions and specifying their semantics using a collection of directed inference rules) and has a more general applicability. It lifts any given abstract domain to include reasoning about a given set of expressions whose semantics is abstracted using a set of axioms. The other domain lifting operation incorporates disjunctive reasoning into a given linear relational abstract domain via introduction of max expressions. We present experimental results demonstrating the potential of the new numerical abstract domain to discover a wide variety of timing bounds (including polynomial, disjunctive, logarithmic, exponential, etc.) for small C programs. © 2008 Springer-Verlag.
CITATION STYLE
Gulavani, B. S., & Gulwani, S. (2008). A numerical abstract domain based on expression abstraction and max operator with application in timing analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5123 LNCS, pp. 370–384). https://doi.org/10.1007/978-3-540-70545-1_35
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