Multi-dimensional Boltzmann Sampling of context-free Languages

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 an extended – multidimensional – version of the classic Boltzmann samplers [7]. We show that, under mostly strong-connectivity hypotheses, our samplers return a word of size in [(1 − ε)n, (1 + ε)n] and exact frequency in O(n) expected time. Moreover, if we accept a tolerance interval of length 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.