This paper addresses the uniform random generation of words from a
context-free language (over an alphabet of size k), while constraining every
letter to a targeted frequency of occurrence. Our approach consists in a
multidimensional extension of Boltzmann samplers \cite{Duchon2004}. We show
that, under mostly \emph{strong-connectivity} hypotheses, our samplers return a
word of size in [(1−ε)n,(1+ε)n] and exact frequency in
O(n1+k/2) expected time. Moreover, if we accept tolerance
intervals of width in Ω(n) for the number of occurrences of each
letters, our samplers perform an approximate-size generation of words in
expected O(n) time. We illustrate these techniques on the
generation of Tetris tessellations with uniform statistics in the different
types of tetraminoes.Comment: 12p
