We are interested in the computing frontier around an essential question about compiler construction: having a program P and a set M of non parametric compiler optimization modules (called also phases), is it possible to find a sequence s of these phases such that the performance (execution time for instance) of the final generated program P′ is "optimal" ? We prove in this article 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 be-comes decidable, and we provide some algorithms (not necessary efficient) that can answer our main question. Another essential question that we are interested in is parame-ters space exploration in optimizing compilation (tuning optimizing compilation parameters). In this case, we assume a fixed sequence of optimization, 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 problem is undecidable and we provide some simplified decidable instances.
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