  Pebble transducers are nested two-way transducers which can drop marks (named
"pebbles") on their input word. Blind transducers have been introduced by
Nguy\^en et al. as a subclass of pebble transducers, which can nest two-way
transducers but cannot drop pebbles on their input.
  In this paper, we study the classes of functions computed by pebble and blind
transducers, when the output alphabet is unary. Our main result shows how to
decide if a function computed by a pebble transducer can be computed by a blind
transducer. We also provide characterizations of these classes in terms of
Cauchy and Hadamard products, in the spirit of rational series. Furthermore,
pumping-like characterizations of the functions computed by blind transducers
are given.
