Iterated Straight-Line Programs
<|reference_start|>Iterated Straight-Line Programs: We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are crucial in areas like Bioinformatics). The extension, called iterated SLPs (ISLPs), allows rules of the form $A \rightarrow \Pi_{i=k_1}^{k_2} B_1^{i^{c_1}}\cdots B_t^{i^{c_t}}$, for which we show how to extract any substring of length $\lambda$, from the represented text $T[1.. n]$, in time $O(\lambda + \log^2 n\log\log n)$. This is the first compressed representation for repetitive texts breaking $\delta$ while, at the same time, supporting direct access to arbitrary text symbols in polylogarithmic time. As a byproduct, we extend Ganardi et al.'s technique to balance any SLP (so it has a derivation tree of logarithmic height) to a wide generalization of SLPs, including ISLPs.<|reference_end|>
@article{navarro2024iterated,
    title={Iterated Straight-Line Programs},
    author={Gonzalo Navarro and Cristian Urbina},
    journal={arXiv preprint arXiv:2402.09232},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09232},
    primaryClass={cs.DS}
}