Iterated Straight-Line Programs

We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure 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 ₈=₊䃑^k₂ B₁^i^{c₁} Bₜ^i^{cₜ}, for which we show how to extract any substring of length, from the represented text T1. . n, in time O (+ ² n n). This is the first compressed representation for repetitive texts breaking 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.