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Non-redundant random generation algorithms for weighted context-free languages

Andy Lorenz 1 Yann Ponty 2, 3, * 
* Corresponding author
3 AMIB - Algorithms and Models for Integrative Biology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
Abstract : We address the non-redundant random generation of $k$ words of length $n$ in a context-free language. Additionally, we want to avoid a predefined set of words. We study a rejection-based approach, whose worst-case time complexity is shown to grow exponentially with $k$ for some specifications and in the limit case of a coupon collector. We propose two algorithms respectively based on the recursive method and on an unranking approach. We show how careful implementations of these algorithms allow for a non-redundant generation of $k$ words of length $n$ in $\mathcal{O}(k\cdot n\cdot \log{n})$ arithmetic operations, after a precomputation of $\Theta(n)$ numbers. The overall complexity is therefore dominated by the generation of $k$ words, and the non-redundancy comes at a negligible cost.
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Submitted on : Thursday, November 1, 2012 - 11:20:57 AM
Last modification on : Sunday, November 20, 2022 - 3:26:55 AM
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Andy Lorenz, Yann Ponty. Non-redundant random generation algorithms for weighted context-free languages. Theoretical Computer Science, 2013, Generation of Combinatorial Structures, 502, pp.177-194. ⟨10.1016/j.tcs.2013.01.006⟩. ⟨inria-00607745v2⟩



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