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

  • Ruiz-Vanoye, Jorge A.
  • Pérez-Ortega, Joaquín
  • R., Rodolfo A. Pazos
  • Díaz-Parra, Ocotlán
  • Fraire-Huacuja, Hector
  • Frausto-Solis, Juan
  • Reyes-Salgado, Gerardo
  • Reyes, Laura Cruz
Abstract:
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.
Research areas:
Year:
2013
Type of Publication:
Article
Keywords:
Formal languages; Polynomial transformations; NP-completeness
Journal:
Journal of Zhejiang University-SCIENCE C (Computers & Electronics)
Volume:
14
Number:
8
Pages:
623-633
ISSN:
1869-196X
DOI:
10.1631/jzus.C1200349
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