A Measure of Space for Computing over the Reals
Paulin Jacobé De Naurois
Abstract
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 NC2\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.
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