Weighted Two-Way Transducers.

Weighted two-way transducers over complete commutative semirings are introduced and investigated. Their computed mappings have two-way definable support. Conversely, for every two-way definable relation R there exists a mapping computable by a weighted two-way transducer whose support is R. It is shown that the class of all such computed mappings is closed under sum and the subclass computed by deterministic weighted two-way transducers is closed under composition.