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<\/i> (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<\/i> 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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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. 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