Complexity invariance of real interpretations

Guillaume Bonfante (1) , Florian Deloup (2)

1 CARTE - Theoretical adverse computations, and safety
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In the field of implicit computational complexity, we are con- sidering 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 complex- ity. We illustrate this by two characterizations, one of PTIME and one of PSPACE.

Domaines: Complexité [cs.CC]

Guillaume Bonfante, Florian Deloup. Complexity invariance of real interpretations. 7th Annual Conference on Theory and Applications of Models of Computation - TAMC 2010, Jun 2010, Prague, Czech Republic. pp.139-150, ⟨10.1007/978-3-642-13562-0⟩. ⟨inria-00535784⟩