  We use higher parallel transport -- more precisely, the integration
A_{infty}-functor constructed by Block-Smith and Arias Abad-Schaetz -- to
define Reidemeister torsion for flat superconnections. We hope that the
combinatorial Reidemeister torsion coincides with the analytic torsion defined
by Mathai and Wu, thus permitting for a generalization of the Cheeger-Mueller
Theorem.
