eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2010-07-06
243
258
10.4230/LIPIcs.RTA.2010.243
article
Polynomial Interpretations over the Reals do not Subsume Polynomial Interpretations over the Integers
Neurauter, Friedrich
Middeldorp, Aart
Polynomial interpretations are a useful technique for proving termination
of term rewrite systems. They come in various flavors:
polynomial interpretations with real, rational and integer coefficients.
In 2006, Lucas proved that there are rewrite systems that can be shown
polynomially terminating by polynomial interpretations with
real (algebraic)
coefficients, but cannot be shown polynomially terminating using
polynomials with rational coefficients only.
He also proved a similar theorem with respect to the use of
rational coefficients versus integer coefficients.
In this paper we show that polynomial interpretations with real or
rational coefficients do not subsume polynomial interpretations with
integer coefficients, contrary to what is commonly believed.
We further show that polynomial interpretations with real
coefficients subsume polynomial interpretations with rational
coefficients.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol006-rta2010/LIPIcs.RTA.2010.243/LIPIcs.RTA.2010.243.pdf
Term rewriting
termination
polynomial interpretations