Recognizable transductions constitute a proper subclass of rational transductions, characterized by the well-known Mezei’s Theorem. We propose a family of transducers which reflect accurately this characterization, and we study their properties and their algorithmic aspects. We base our construct on the observation that there is a connection between recognizable transductions and languages cons...

Local deterministic string-to-string transductions are generalizations of morphisms on free monoids. Learning local transductions reduces to inference of monoid morphisms. However, learning a restricted class of morphisms, the so-called fine morphisms, is an intractable problem, because the decision version of the empirical risk minimization problem contains an NP-complete subproblem.

We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

Deterministic two-way transducers on finite words have been shown by Engelfriet and Hoogeboom to have the same expressive power as MSO-transductions. We introduce a notion of aperiodicity for these transducers and we show that aperiodic transducers correspond exactly to FO-transductions. This lifts to transducers the classical equivalence for languages between FO-definability, recognition by ap...

We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

A sensitive and fully DNA-structured ion sensor was built by integrating polyT sequences for highly selective Hg2+ recognitions and two flanking G-quadruplex halves for allosteric signal transductions. The construction of this sensor was very easy that allowed a cost-effective detection of Hg2+ with a limit of detection of 4.5 nM, which was lower than the 10 nM toxic level for drinkable water a...