Complexity invariance of real interpretations

Authors:
Guillaume Bonfante;Florian Deloup
Affiliations:
LORIA, Université de Nancy, Nancy, France;Toulouse - IMT, Université Paul Sabatier, France
Venue:
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Year:
2010

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Abstract

In the field of implicit computational complexity, we are considering in this paper the fruitful branch of interpretation methods In this area, the synthesis problem is solved by Tarski's decision procedure, and consequently interpretations are usually chosen over the reals rather than over the integers Doing so, one cannot use anymore the (good) properties of the natural (well-) ordering of N employed to bound the complexity of programs We show that, actually, polynomials over the reals benefit from some properties that allow their safe use for complexity We illustrate this by two characterizations, one of PTIME and one of PSPACE.