Straight-line grammar

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A straight-line grammar (sometimes with "straight-line" in scare quotes,[1] also abbreviated as SLG) is a formal grammar that generates exactly one string.[2] 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).[2]

SLGs are of interest in fields like Kolmogorov complexity, Lossless data compression, Structure discovery and Compressed data structures.[clarification needed]

The problem of finding a context-free SLG of minimal size that generates a given string is called the smallest grammar problem.[citation needed]

Formal Definition[edit]

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

2. the directed graph G=<V,E>, defined by V being the set of non-terminals and (A,B) ∈ E whenever B appears at the right-hand side of a production rule for A, is acyclic.[3][not in citation given]

An SLG in Chomsky normal form is equivalent[clarification needed] to a straight-line program.

A list of algorithms using SLGs[edit]

See also[edit]


  1. ^
  2. ^ a b Florian Benz and Timo Kötzing, “An effective heuristic for the smallest grammar problem,” Proceeding 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
  3. ^ Markus Lohrey; Sebastian Maneth; Manfred Schmidt-Schauß (2009). "Parameter Reduction in Grammar-Compressed Trees". Proc. FOSSACS (PDF). LNCS. 5504. Springer. pp. 212–226.  Here: p.215, Sect.2