Abstract

We provide a fairly complete picture of the complexity theory of additive real machines. This model of computation is a restriction of the real Turing machine of Blum et al. (1989), since addition and subtraction are the only legal arithmetic operations. Removing the order relation < on R yields an even weaker class of machines, which is also studied. Our main results are: • characterization of the classes of recognizable Boolean languages; • equivalence of real and digital nondeterminism; • a simpler proof of Meer's P lin ≠ NP lin result.

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