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A straight-line grammar (sometimes abbreviated as SLG) is a formal grammar that generates exactly one string. Consequently, it does not branch (every non-terminal has only one associated production rule) nor loop (if non-terminal A appears in a derivation of B, then B does not appear in a derivation of A).
Areas of usefulness
Straight-line grammars are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression).:212
Straight-line grammars (more precisely: straight-line context-free string grammars) can be generalized to Straight-line context-free tree grammars. The latter can be used conveniently to compress trees.:212
A context-free grammar G is an SLG if:
1. for every non-terminal N, there is at most one production rule that has N as its left-hand side, and
A mathematical definition of the more general formalism of straight-line context-free tree grammars can be found in Lohrey et al.:215
A list of algorithms using SLGs
- The Sequitur algorithm constructs a straight-line grammar for a given string.
- The Lempel-Ziv-Welch algorithm creates a context-free grammar in such a deterministic way that it is necessary to store only the start rule of the generated grammar.
- Byte pair encoding
- Grammar-based code
- Non-recursive grammar - a grammar that doesn't loop, but may branch; generating a finite rather than a singleton language
- Florian Benz and Timo Kötzing, “An effective heuristic for the smallest grammar problem,” Proceedings of the fifteenth annual conference on Genetic and evolutionary computation conference - GECCO ’13, 2013. ISBN 978-1-4503-1963-8 doi:10.1145/2463372.2463441, p. 488
- Markus Lohrey; Sebastian Maneth; Manfred Schmidt-Schauß (2009). "Parameter Reduction in Grammar-Compressed Trees". Proc. FOSSACS (PDF). LNCS. 5504. Springer. pp. 212–226.
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