Reducing the Size of the Constraint Model in Implicit Path Enumeration Using Super Blocks

Implicit Path Enumeration (IPE) is the most popular calculation technique used in WCET analysis as it generally provides the most precision. It utilises the Control Flow Graph (CFG) to build a constraint system consisting of, amongst others, structural constraints (derived from the CFG) and relative capacity constraints (loop bounds relative to the innermost enclosing loop). However, solving the constraint system is an NP-hard problem and reducing the size of the model is therefore desirable. This paper shows that, when the CFG loops are free of break-like constructs, the constraint system produced by IPE consists of many superfluous structural constraints in that their elimination does not detract from the precision of the WCET estimate. We demonstrate this fact by building an alternative constraint system from a new intermediate data structure called the Super Block Control Flow Graph (SB-CFG). Furthermore, we illustrate how the SB-CFG allows us to deduce when relative capacity constraints are actually needed -- until now they have been considered mandatory to avoid overestimations with loops. Comparing the two constraint systems across a large number of automatically generated control flow graphs, our results show there is: a 50% reduction in the number of variables, a 55% reduction in the number of constraints, and a 69% reduction in solving time.