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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2010

Multi-dimensional Boltzmann Sampling of Languages


We address 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. We show that, under mostly $\textit{strong-connectivity}$ hypotheses, our samplers return a word of size in $[(1- \epsilon)n, (1+ \epsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega (\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate our approach on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.
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Dates and versions

hal-00450763 , version 1 (30-01-2010)
hal-00450763 , version 2 (01-03-2010)
hal-00450763 , version 3 (01-06-2010)
hal-00450763 , version 4 (20-08-2015)



Olivier Bodini, Yann Ponty. Multi-dimensional Boltzmann Sampling of Languages. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), Jun 2010, Vienna, Austria. pp.49-64, ⟨10.46298/dmtcs.2793⟩. ⟨hal-00450763v4⟩
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