The Light Lexicographic path Ordering

We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space bounded by a polynomial in the size of the inputs

Polynomials over the reals are safe for program interpretations

In the field of implicit computational complexity, we are con- sidering in this paper the fruitful branch of interpretation methods. Due to their good intensional properties, they have been widely developped. Among usual issues is the synthesis problem which has been solved by the use of 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 allows their safe use for complexity. We illustrate this by two char- acterizations, one of PTIME and one of PSPACE