Does there exist the idea of “RP-complete”, like NP-complete?

NP-hardness and NP-completeness play an important role in complexity theory. My question is, does there exist a language $L$ in RP to which any language $M$ in RP can be reduced in polynomial time? We can say that such a language $L$ is "RP-complete", if exists, but I cannot find any information about this idea. Can anyone tell me about it, please?

• This question is not research level. Should have been migrated to computer science stack exchange. – Tayfun Pay Jan 2 '14 at 18:14
• @TayfunPay given that this is an open problem, I think it should be considered research level. – Sasho Nikolov Jan 2 '14 at 18:30
• @TayfunPay Borderline. The literal question being asked (essentially, is there such a thing of RP-completeness) is not research-level but the closely related question of whether any such problems exist appears to be open so is research-level. – David Richerby Jan 2 '14 at 18:33
• @TayfunPay Sorry about that. Maybe I should have posted this on CS stack exchange. However, thanks to David Richerby's helpful answer and others' comments, I think now this topic has research-level value as a whole, so I want to keep it on this site. Any way, I'll be careful on which site to post a new question. Thanks. – Kota Ishihara Jan 2 '14 at 19:00
• If you open any good computational complexity book and read it, you will get the answer for this question. So in my opinion, it is still not research level. I have seen numerous questions down voted for the same reason. – Tayfun Pay Jan 3 '14 at 2:56

• @David: you can weaken the definition of "BPP-complete" such that it makes sense for approximation problems to be "BPP-complete". You can then find lots of interesting "BPP-complete" approximation problems. People who insist that only decision problems can be be BPP-complete are leaving vast areas of interesting complexity theory completely unexplored. Such a BPP-complete approximation problem should be both BPP-hard and solvable in $\mathrm{P}^\mathrm{BPP}$. Rephrasing my question, does a similar phenomenon exist with RP? – Peter Shor Jan 2 '14 at 18:15