A straight-line grammar (sometimes abbreviated as SLG) is a formal grammar that generates exactly one string.[1] 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).[1]
Straight-line grammars are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression).[2]
SLGs are of interest in fields like Kolmogorov complexity, Lossless data compression, Structure discovery and Compressed data structures.
The problem of finding a context-free grammar (equivalently: an SLG) of minimal size that generates a given string is called the smallest grammar problem.
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.[2]
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.
A mathematical definition of the more general formalism of straight-line context-free tree grammars can be found in Lohrey et al.[2]
An SLG in Chomsky normal form is equivalent to a straight-line program.