Straight-line grammar

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 an SLG of minimal size that generates a given string is called the Smallest grammar problem.[citation needed]

Formal Definition

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 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.