We are interested in the computing frontier around an essential question about compiler construction: having a program and a set of non-parametric compiler optimization modules (also called phases), is it possible to find a sequence *s* of these phases such that the performance (for instance, execution time) of the final generated program ′ is *optimal*? We proved in [TOU 06] that this problem is undecidable in two general schemes of optimizing compilation: iterative compilation and library optimization/generation. Fortunately, we give some simplified cases when this problem becomes decidable, and we provide some algorithms (not necessarily efficient) that can answer our main question.

Another essential problem that we are interested in is parameter space exploration in optimizing compilation (tuning optimizing compilation parameters). In this case, we assume a fixed sequence of compiler optimizations, but each optimization phase is allowed to have a parameter. We try to figure out how to compute the best parameter values for all program transformations when the compilation sequence is given. We also prove that this general ...

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