Discrete log accumulator without pairings?
Sure.  Use the strong RSA assumption.  The accumulator of $x_1,\dots,x_k$ is $A = g^{x_1 x_2 \cdots x_k} \bmod n$, where $n$ is a RSA modulus and $g$ is a fixed base.  To prove that the accumulator $A$ contains $x$, exhibit a value $h$ such that $h^x=A \pmod n$.  This is secure under the strong RSA assumption, and has a discrete log "feel" to it.