Well, you can't solve it in the general case. But parallelizing compilers can and have been written that perform a conservative analysis -- they can prove some

Well, you can't solve it in the general case. But parallelizing compilers can and have been written that perform a conservative analysis -- they can prove some subset of all parallelizable loops as parallelizable, and for the ones they can't prove as such, they err toward 'remain serialized'. For a simple example, code that performs regular array-based accesses, where index computations are simple affine functions (a*i + b) of a single iteration variable 'i', is a case that's received a lot of attention. See e.g. Polly for LLVM.