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

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.

arXiv admin note: text overlap with arXiv:1012.4560

References in corpus (3)

• Controlled non uniform random generation of decomposable structures
• Multi-dimensional Boltzmann Sampling of Languages
• On the Average Complexity of Moore's State Minimization Algorithm