  The Neural Turing Machine (NTM) is more expressive than all previously
considered models because of its external memory. It can be viewed as a broader
effort to use abstract external Interfaces and to learn a parametric model that
interacts with them.
  The capabilities of a model can be extended by providing it with proper
Interfaces that interact with the world. These external Interfaces include
memory, a database, a search engine, or a piece of software such as a theorem
verifier. Some of these Interfaces are provided by the developers of the model.
However, many important existing Interfaces, such as databases and search
engines, are discrete.
  We examine feasibility of learning models to interact with discrete
Interfaces. We investigate the following discrete Interfaces: a memory Tape, an
input Tape, and an output Tape. We use a Reinforcement Learning algorithm to
train a neural network that interacts with such Interfaces to solve simple
algorithmic tasks. Our Interfaces are expressive enough to make our model
Turing complete.
