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On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In the seventies, Manna and Ness, Lankford, and Dershowitz pionneered the use of polynomial interpretations with integer and real coefficients in proofs of termination of rewriting. More than twenty five years after these works were published, however, the absence of true examples in the literature has given rise to some doubts about the possible benefits of using polynomials with real or rational coefficients. In this paper we prove that there are, in fact, rewriting systems that can be proved polynomially terminating by using polynomial interpretations with (algebraic) real coefficients; however, the proof cannot be achieved if polynomials only contain rational coefficients. We prove a similar statement with respect to the use of rational coefficients versus integer coefficients.

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  1. DSIC, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    Salvador Lucas

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Lucas, S. On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting. AAECC 17, 49–73 (2006). https://doi.org/10.1007/s00200-005-0189-5

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  • DOI: https://doi.org/10.1007/s00200-005-0189-5

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