Frameworks for logically classifying polynomial-time optimisation problems

  • Authors:

  • James Gate;Iain A. Stewart

  • Affiliations:

  • School of Engineering and Computing Sciences, Durham University, Science Labs, Durham, U.K.;School of Engineering and Computing Sciences, Durham University, Science Labs, Durham, U.K.

  • Venue:
  • CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P≠NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems.