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2010
Springer

Frameworks for Logically Classifying Polynomial-Time Optimisation Problems

9 years 8 months ago
Frameworks for Logically Classifying Polynomial-Time Optimisation Problems
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 NPcomplete. 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.
James Gate, Iain A. Stewart
Added 19 Jul 2010
Updated 19 Jul 2010
Type Conference
Year 2010
Where CSR
Authors James Gate, Iain A. Stewart
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