A problem is Friendly AI-complete if solving it is equivalent to creating Friendly AI.

The Machine Intelligence Research Institute argues that any safe superintelligence architecture is FAI-complete. For example, the following have been proposed as hypothetical safe AGI designs:

Oracle AI - an AGI which takes no action besides answering questions.
Tool AI - an AGI which isn't an independent decision-maker at all, but is rather "just a calculator".
Nanny AI - an AGI of limited superintelligence, restricted to preventing more advanced AGIs from arising until safer AGIs are developed.

In "Dreams of Friendliness" Eliezer Yudkowsky argues that if you have an Oracle AI, then you can ask it, "What should I do?" If it can answer this question correctly, then it is FAI-complete.

Similarly, if you have a tool AI, it must make extremely complex decisions about how many resources it can use, how to display answers in human understandable yet accurate form, et cetera. The many ways in which it could choose catastrophically require it to be FAI-complete. Note that this does not imply that an agent-like, fully free FAI is easier to create than any of the other proposals.

Goertzel proposed a "Nanny AI"(Should humanity build a global AI nanny to delay the singularity until it’s better understood?) with moderate superhuman intelligence, able to forestall Singularity eternally, or to delay it. However, it has been argued by Luke Muehlhauser and Anna Salamon (Intelligence Explosion: Evidence and Import) that a Nanny AI is FAI-complete. They claim that building it could require solving all the problems required to build Friendly Artificial Intelligence.

Blog posts

Dreams of Friendliness
Reply to Holden on 'Tool AI'
A Taxonomy of Oracle AIs

References

Should humanity build a global AI nanny to delay the singularity until it’s better understood? by Ben Goertzel
Intelligence Explosion: Evidence and Import by Luke Muehlhauser and Anna Salamon

See also

FAI
AI-complete