Symbolic simulation on complicated loops for WCET path analysis

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Abstract
We address the Worst-Case Execution Time (WCET) Path Analysis problem for bounded programs, formalized as discovering a tight upper bound of a resource variable. A key challenge is posed by complicated loops whose iterations exhibit non-uniform behavior. We adopt a brute-force strategy by simply unrolling them, and show how to make this scalable while preserving accuracy. Our algorithm performs symbolic simulation of the program. It maintains accuracy because it preserves, at critical points, path-sensitivity. In other words, the simulation detects infeasible paths. Scalability, on the other hand, is dealt with by using summarizations, compact representations of the analyses of loop iterations. They are obtained by a judicious use of abstraction which preserves critical information flowing from one iteration to another. These summarizations can be compounded in order for the simulation to have linear complexity: the symbolic execution can in fact be asymptotically shorter than a concrete execution. Finally, we present a comprehensive experimental evaluation using a standard benchmark suite. We show that our algorithm is fast, and importantly, we often obtain not just accurate but exact results.

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