Abstract
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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Acknowledgments
We are extremely grateful to an anonymous referee for helping to make this a better paper. We are also grateful to S. Bosio, E. Goubault, J. Leconte, A. Lodi, D. Monniaux, F. Roda, F. Raimondi, S. Le Roux for useful discussions, during the course of several years. This work was financially supported by the following Grants: ANR “ARS”, ANR “ASOPT”, Digiteo “PASO” and Digiteo “RMNCCO”.
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Dedicated to Panos Pardalos, eclectic theoretical computer scientist and global optimizer, on the occasion of his 60th birthday.
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Liberti, L., Marinelli, F. Mathematical programming: Turing completeness and applications to software analysis. J Comb Optim 28, 82–104 (2014). https://doi.org/10.1007/s10878-014-9715-3
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DOI: https://doi.org/10.1007/s10878-014-9715-3