  The input/output complexity, which is the complexity of data exchange between
the main memory and the external memory, has been elaborately studied by a lot
of former researchers. However, the existing works failed to consider the
input/output complexity in a computation model point of view. In this paper we
remedy this by proposing three variants of Turing machine that include external
memory and the mechanism of exchanging data between main memory and external
memory. Based on these new models, the input/output complexity is deeply
studied. We discussed the relationship between input/output complexity and the
other complexity measures such as time complexity and parameterized complexity,
which is not considered by former researchers. We also define the external
access trace complexity, which reflects the physical behavior of magnetic disks
and gives a theoretical evidence of IO-efficient algorithms.
