Journal of Zhejiang University SCIENCE C

, Volume 14, Issue 8, pp 623–633 | Cite as

Application of formal languages in polynomial transformations of instances between NP-complete problems

  • Jorge A. Ruiz-VanoyeEmail author
  • Joaquín Pérez-Ortega
  • Rodolfo A. Pazos Rangel
  • Ocotlán Díaz-Parra
  • Héctor J. Fraire-Huacuja
  • Juan Frausto-Solís
  • Gerardo Reyes-Salgado
  • Laura Cruz-Reyes


We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson’s. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.

Key words

Formal languages Polynomial transformations NP-completeness 

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jorge A. Ruiz-Vanoye
    • 1
    Email author
  • Joaquín Pérez-Ortega
    • 2
  • Rodolfo A. Pazos Rangel
    • 3
  • Ocotlán Díaz-Parra
    • 1
  • Héctor J. Fraire-Huacuja
    • 3
  • Juan Frausto-Solís
    • 4
  • Gerardo Reyes-Salgado
    • 5
  • Laura Cruz-Reyes
    • 3
  1. 1.DACIUniversidad Autónoma del CarmenCd. del CarmenMexico
  2. 2.Computer ScienceCentro Nacional de Investigación y Desarrollo TecnológicoCuernavacaMexico
  3. 3.Systems and Computer ScienceInstituto Tecnológico de Ciudad MaderoCiudad MaderoMexico
  4. 4.InformaticsUniversidad Politécnica del Estado de MorelosJiutepecMexico
  5. 5.Computer ScienceInstituto Tecnológico de CuautlaCuautlaMexico

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