Mathematical Programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of Mathematical Programming to software verification obtained by relaxing one of the properties of Turing complete languages.

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View Mathematical Programming: Turing completeness and applications to software analysis