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 that has support R and is computable by a weighted two-way transducer. The class of all such computed mappings is naturally closed under sum. Finally, both the subclass computed by deterministic weighted two-way transducers and the subclass computed by unambiguous weighted two-way transducers are shown to be closed under composition, pseudo HADAMARD product, unambiguous CAUCHY product, and unambiguous KLEENE iteration.(c) 2023 Elsevier Inc. All rights reserved.