  Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual
computation protocol recently proposed by Hosten et al. is counterfactual for
only one output of the computer. This claim was based on the existing abstract
algebraic definition of counterfactual computation, and indeed according to
this definition, their argument is correct. However, a more general definition
(physically adequate) for counterfactual computation is implicitly assumed by
Hosten et. al. Here we explain in detail why the protocol is counterfactual and
how the "history tracking" method of the existing description inadequately
represents the physics underlying the protocol. Consequently, we propose a
modified definition of counterfactual computation. Finally, we comment on one
of the most interesting aspects of the error-correcting protocol.
