  Homotopy classes of nanowords and nanophrases are combinatorial
generalizations of virtual knots and links. Goussarov, Polyak and Viro defined
finite type invariants for virtual knots and links via semi-virtual crossings.
We extend their definition to nanowords and nanophrases. We study finite type
invariants of low degrees. In particular, we show that the linking matrix and T
invariant defined by Fukunaga are finite type of degree one and degree two
respectively. We also give a finite type invariant of degree 4 for open
homotopy of Gauss words.
