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CADE
2010
Springer

Monotonicity Criteria for Polynomial Interpretations over the Naturals

8 years 6 months ago
Monotonicity Criteria for Polynomial Interpretations over the Naturals
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. In an automated setting, termination tools are concerned with parametric polynomials whose coefficients (i.e., the parameters) are initially unknown and have to be instantiated suitably such that the resulting concrete polynomials satisfy certain conditions. We focus on monotonicity and well-definedness, the two main conditions that are independent of the respective term rewrite system considered, and provide constraints on the abstract coefficients for linear, quadratic and cubic parametric polynomials such that monotonicity and well-definedness of the resulting concrete polynomials are guaranteed whenever the constraints are satisfied. Our approach subsumes the absolute positiveness approach, which is currently used in many termination tools. In particular, it allows for negative numbers in certain coefficients. We also give an example of a term rewrite system whose termination proof...
Friedrich Neurauter, Aart Middeldorp, Harald Zankl
Added 13 Jan 2011
Updated 13 Jan 2011
Type Journal
Year 2010
Where CADE
Authors Friedrich Neurauter, Aart Middeldorp, Harald Zankl
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