A Measure of Space for Computing over the Reals

Paulin Jacobé de Naurois (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

We propose a new complexity measure of space for the BSS model of computation. We define LOGSPACE_W and PSPACE_W complexity classes over the reals. We prove that LOGSPACE_W is included in NC^2_R and in P_W, i.e. is small enough for being relevant. We prove that the Real Circuit Decision Problem is P_R-complete under LOGSPACE_W reductions, i.e. that LOGSPACE_W is large enough for containing natural algorithms. We also prove that PSPACE_W is included in PAR_R.

Mots clés: BSS model of computation; weak model; algebraic complexity; space

Domaines: Complexité [cs.CC]

Paulin Jacobé de Naurois. A Measure of Space for Computing over the Reals. Logical Approaches to Computational Barriers Second Conference on Computability in Europe, CiE 2006, 2006, Swansea, United Kingdom. pp.231-240. ⟨hal-00020024v2⟩