### March 12, 2018

**Luc Dartois**(ULB)

In this talk I present a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. I argue that LT is a suitable candidate as a specification language for verification of non reactive systems, extending the successful approach of verifying synchronous systems via Mealy Machines and MSO.

In LT, the input/output dependencies are modelled via an origin function which associates to any position of the output word, the input position from which it originates. LT is well-suited to express relations (which are not necessarily functional), and can express all regular functional transductions, i.e. transductions definable for instance by deterministic two-way transducers.

Despite its high expressive power, LT has decidable satisfiability problems. The main contribution is a synthesis result: it is always possible to synthesis a regular function which satisfies the specification.

Finally, I explicit a correspondence between transductions and data words. As a side-result, we obtain a new decidable logic for data words.