IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v28y2014i1d10.1007_s10878-014-9715-3.html
   My bibliography  Save this article

Mathematical programming: Turing completeness and applications to software analysis

Author

Listed:
  • Leo Liberti

    (IBM “T.J. Watson” Research Center
    École Polytechnique)

  • Fabrizio Marinelli

    (Università Politecnica delle Marche)

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.

Suggested Citation

  • Leo Liberti & Fabrizio Marinelli, 2014. "Mathematical programming: Turing completeness and applications to software analysis," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 82-104, July.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-014-9715-3
    DOI: 10.1007/s10878-014-9715-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9715-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-014-9715-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. C. Jeroslow, 1973. "There Cannot be any Algorithm for Integer Programming with Quadratic Constraints," Operations Research, INFORMS, vol. 21(1), pages 221-224, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leo Liberti & Benedetto Manca, 2022. "Side-constrained minimum sum-of-squares clustering: mathematical programming and random projections," Journal of Global Optimization, Springer, vol. 83(1), pages 83-118, May.
    2. David E. Bernal & Zedong Peng & Jan Kronqvist & Ignacio E. Grossmann, 2022. "Alternative regularizations for Outer-Approximation algorithms for convex MINLP," Journal of Global Optimization, Springer, vol. 84(4), pages 807-842, December.
    3. Maurizio Bruglieri & Roberto Cordone & Leo Liberti, 2022. "Maximum feasible subsystems of distance geometry constraints," Journal of Global Optimization, Springer, vol. 83(1), pages 29-47, May.
    4. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ngueveu, Sandra Ulrich, 2019. "Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1058-1071.
    2. Sönke Behrends & Anita Schöbel, 2020. "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 911-935, September.
    3. Sirmatel, Isik Ilber & Geroliminis, Nikolas, 2018. "Mixed logical dynamical modeling and hybrid model predictive control of public transport operations," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 325-345.
    4. Sönke Behrends & Ruth Hübner & Anita Schöbel, 2018. "Norm bounds and underestimators for unconstrained polynomial integer minimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 73-107, February.
    5. Tiago Andrade & Fabricio Oliveira & Silvio Hamacher & Andrew Eberhard, 2019. "Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming," Journal of Global Optimization, Springer, vol. 73(4), pages 701-722, April.
    6. Albers, Sönke & Brockhoff, Klaus, 1979. "Optimal product attributes in single choice models," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 67, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Hamidur Rahman & Ashutosh Mahajan, 2020. "On the facet defining inequalities of the mixed-integer bilinear covering set," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 545-575, December.
    8. Shang, You-lin & Zhang, Lian-sheng, 2008. "Finding discrete global minima with a filled function for integer programming," European Journal of Operational Research, Elsevier, vol. 189(1), pages 31-40, August.
    9. Hoai Le Thi & Duc Tran, 2014. "Optimizing a multi-stage production/inventory system by DC programming based approaches," Computational Optimization and Applications, Springer, vol. 57(2), pages 441-468, March.
    10. Claudia D’Ambrosio & Andrea Lodi, 2013. "Mixed integer nonlinear programming tools: an updated practical overview," Annals of Operations Research, Springer, vol. 204(1), pages 301-320, April.
    11. Jesús A. De Loera & Raymond Hemmecke & Matthias Köppe & Robert Weismantel, 2006. "Integer Polynomial Optimization in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 147-153, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-014-9715-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.