Abstract. The determination of upper bounds on execution times, commonly called WorstCase Execution Times (WCETs), is a necessary step in the development and validation process for hard real-time systems. This problem is hard if the underlying processor architecture has components such as caches, pipelines, branch prediction, and other speculative components. This article describes different approaches to this problem and surveys several commercially available tools and research prototypes.

We present a family of abstract-interpretation algorithms that are capable of determining \shape invariants" of programs that perform destructive updating on dynamically allocated storage. The main idea is to represent the stores that can possibly arise during execution using three-valued logical structures.Questions about properties of stores can be answered by evaluating predicate-logic formulae using Kleene's semantics of three-valued logic:If a formula evaluates to true, then the formula holds in every store represented by the three-valued structure. If a formula evaluates to false, then the formula does not hold in any store represented by the three-valued structure.If a formula evaluates to unknown, then we do not know if this formula always holds, never holds, or sometimes holds and sometimes does not hold in the stores represented by the three-valued structure. Three-valued logical structures are thus a conservative representation of memory stores.The approach described is a parametric framework: It provides the basis for generating a family of shape-analysis algorithms by varying the vocabulary used in the three-valued logic.

We present a family of abstract-interpretation algorithms that are capable of determining "shape invariants" of programs that perform destructive updating on dynamically allocated storage. The main idea is to represent the stores that can passibly arise during execution using three-valued logical structures.Questions about properties of stores can be answered by evaluating predicate-logic formulae using Kleene's semantics of three-valued logic:l If a formula evaluates to true, then the formula holds in every store represented by the three-valued structure.l If a formula evaluates to false, then the formula does not hold in any store represented by the three-valued structure.l If a formula evaluates to unknown, then we do not know if this formula always holds, never holds, or sometimes holds and sometimes does not hold in the stores represented by the three-valued structure.Three-valued logical structures are thus a conservative representation of memory stores. The approach described is a parametric framework: It provides the basis for generating a family of shape-analysis algorithms by varying the vocabulary used in the three-valued logic.Permission to make digital or hard copies of all or parl ufthis work for personal or classroom me is granted withwt fee procided that copies are not made or distrihutcd for profit or cnrnmercinl advantage IIKI that copies bear this notice and the full citation on the first page. To copy otherwise. to republid~, to post on sewers or to redistribute tn lists, requires prior specific permission anJ!or a fee.

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