Here $g$ is some fixed generator of a discrete log group. I don't want the group to be bilinear for efficiency and BDH-skepticism reasons.
Is anyone aware of a discrete log accumulator? What I mean specifically is some function $f(x, A)\mapsto A'$ (that is, $A$ is the accumulator value; $f$ adds $x$ to the accumulator, changing its value to $A'$) such that given $(g^x, A')$ anyone can check whether $x$ was placed in the accumulator.
So I'm roughly asking for an accumulator with the property that an accumulated element $x$ has $g^x$ as a witness.