Iterated Straight-Line Programs

We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure δ 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 → Πi=k₁k₂ B₁^ic₁⋯ Bₜ^icₜ, for which we show how to extract any substring of length λ, from the represented text $T[1.. n]$, in time O(λ + log² nloglog n). This is the first compressed representation for repetitive texts breaking δ 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.