Constructive reduction: understanding uncomputability through programming

  • Authors:
  • Jesús Ibáñez;Ana Sánchez

  • Affiliations:
  • Basque Country University, Donostia, Spain;Basque Country University, Donostia, Spain

  • Venue:
  • ACM SIGCSE Bulletin
  • Year:
  • 2009

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Abstract

We present a programming approach to teach the reduction technique in a computing engineering degree's Computability Theory course. It is based in a computing formalism that allows the students to analyze, construct and transform programs as normal data in a simple way. Reduction can then be tackled in a constructive manner, so that the students benefit from their programming skills to prove uncomputability results without the help of the Parametrization (S-m-n) Theorem. Additionally the method is suitable to be applied to interesting problems that cannot be handled by diagonalization nor classical reduction.