Transducers with origin information

Call a string-to-string transducer regular if it can be realised by one of the following equivalent models: mso transductions, two-way deterministic automata with output, and streaming transducers with registers. This paper proposes to treat origin information as part of the semantics of a regular string-to-string transducer. With such semantics, the model admits a machine-independent characterisation, Angluin-style learning in polynomial time, as well as effective characterisations of natural subclasses such as one-way transducers or first-order definable transducers.