On the Structure of $\cal NP_\Bbb C$
Gregorio Malajovich, Klaus Meer · SIAM Journal on Computing · 1998
This paper deals with complexity classes ${\cal P}_{\Bbb C}$ and ${\cal NP}_{\Bbb C}$ as they were introduced over the complex numbers by Blum, Shub, and Smale [Bull. Amer. Math. Soc., 21 (1989), p. 1]. Under the assumption ${\cal P}_{\Bbb C} e {\cal NP}_{\Bbb C}$ the existence of noncomplete problems in ${\cal NP}_{\Bbb C}$ not belonging to ${\cal P}_{\Bbb C}$ is established.