An Embedding of the BSS Model of Computation in Light Affine Lambda-Calculus [article]

Patrick Baillot, Marco Pedicini
2006 arXiv   pre-print
This paper brings together two lines of research: implicit characterization of complexity classes by Linear Logic (LL) on the one hand, and computation over an arbitrary ring in the Blum-Shub-Smale (BSS) model on the other. Given a fixed ring structure K we define an extension of Terui's light affine lambda-calculus typed in LAL (Light Affine Logic) with a basic type for K. We show that this calculus captures the polynomial time function class FP(K): every typed term can be evaluated in
more » ... al time and conversely every polynomial time BSS machine over K can be simulated in this calculus.
arXiv:cs/0608040v1 fatcat:zpyjpm7iafd6zfpvbytnuz3xqu