  We show that if $\mathbb A$ is a core relational structure such that
CSP($\mathbb A$) can be solved by a linear Datalog program, and $\mathbb A$ is
$n$-permutable for some $n$, then CSP($\mathbb A$) can be solved by a symmetric
Datalog program (and thus CSP($\mathbb A$) lies in deterministic logspace). At
the moment, it is not known for which structures $\mathbb A$ will CSP($\mathbb
A$) be solvable by a linear Datalog program. However, once somebody obtains a
characterization of linear Datalog, our result immediately gives a
characterization of symmetric Datalog.
