I am wondering what is known about the complexity of the reversible Circuit Value Problem (rCVP) and the corresponding reversible Satisfiability problem (rSAT).
More precisely: a circuit $B^n\rightarrow B^n$ on $n$ boolean values is reversible if it computes an invertible function.
The rCVP problem is: given a reversible circuit on $n$ boolean values and $n$ inputs, what is the value of the output?
The rSAT problem is: given a reversible circuit, what is the input that yields the output $1,\dots,1$? (function problem, see comments)
As subcases of their non-reversible versions (CVP and SAT) these problem are respectively in Ptime and NP.
My question is rather about hardness: is rCVP Ptime-complete? Is rSAT NP-complete? I am no specialist of this and looked for a statement of the result, but found nothing so far. I read that one can encode any usual circuit by a reversible circuit using Toffoli's gates, but the is size of the reversible circuit one obtains doing so polynomial in the size of the initial circuit?