In computer science, a prefix grammar is a grammar, akin to the formal grammars, where strings are built up from a set of base strings by continually replacing prefixes. The prefix grammars describe exactly all regular languages.

Formal definition

A prefix grammar G is a 3-tuple, (Σ, S, P), where

• Σ is a finite alphabet
• S is a finite set of base strings over Σ
• P is a set of productions of the form u → v where u and v are strings over Σ

Each production u → v can only be applied to a string of the form uw.

Example

One simple prefix grammar can be defined by

• Σ = {0, 1}
• S = {01, 10}
• P = {0 → 010, 10 → 100}

which describes the language defined by the regular expression