Concetti Chiave
Generalized Straight-Line Programs (GSLPs) can be balanced to have height O(log n) without asymptotically increasing their size. Iterated SLPs (ISLPs), a specialized form of GSLPs, can represent some text families in size o(δ) while supporting efficient substring extraction and other queries.
Sintesi
The content discusses the development of a new class of grammars called Generalized Straight-Line Programs (GSLPs) that can be efficiently balanced without increasing their asymptotic size. GSLPs extend traditional Straight-Line Programs (SLPs) by allowing special rules of the form A→x, where x is a program (in any Turing-complete language) that outputs a sequence of variables.
The authors then introduce a specialized form of GSLPs called Iterated SLPs (ISLPs), which allow more complex iteration rules of the form A→Πk2i=k1Bic1
1 ... Bict
t. They show that ISLPs can represent some text families in size o(δ), where δ is a lower-bounding measure of repetitiveness, while still supporting efficient substring extraction and other queries.
Specifically:
- The authors prove that any balanceable GSLP can be transformed into an equivalent GSLP of the same asymptotic size but with a derivation tree of height O(log n).
- They introduce ISLPs, a specialized form of GSLPs, and show that some text families can be represented by an ISLP of size O(δ/√n), breaking the Ω(δ) barrier.
- Using the balancing property of GSLPs, they show that ISLPs can extract any substring of length λ in time O(λ + log^2 n log log n), as well as compute various substring queries in time O(log^2 n log log n).
- They further specialize ISLPs to Run-Length SLPs (RLSLPs), and show how to efficiently compute a wide class of "composable" substring queries, such as Karp-Rabin fingerprints, in time O(log n).
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