Multi-tape Computing with Synchronous Relations

We sketch an approach to encode relations of arbitrary arity as simple languages. Our main focus will be faithfulness of the encoding: we prove that with normal finite-state methods, it is impossible to properly encode the full class of rational (i.e. transducer recognizable) relations; however, there is a simple encoding for the synchronous rational relations. We present this encoding and show how standard finite-state methods can be used with this encoding, that is, arbitrary operations on relations can be encoded as operations on the code. Finally we sketch an implementation using an existing library (FOMA).