Decidable Logics for Transductions and Data Words.

We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modeled via an origin function which associates with any position of the output word, the input position from which it originates. The logic LT can express all MSO-definable functions, and is incomparable with MSO-transducers for relations. Despite its high expressive power, we show, among other interesting properties, that LT has decidable satisfiability and equivalence problems. The transduction logic LT is shown to be expressively equivalent to a logic for data words, LD, up to some bijection from transductions with origin to data words (the origin of an output position becomes the data of that position). The logic LD, which is interesting in itself and extends in expressive power known logics for data words, is shown to have decidable satisfiability.