Regular Grammar

A regular grammar is a restricted form of formal grammar in which every production rule has a single non-terminal on the left-hand side and, on the right-hand side, either a single terminal, a terminal followed by a single non-terminal, or the empty string. This right-linear (or equivalently left-linear) form is precisely what makes the grammar generate only regular languages — no unbounded nesting, no context-sensitive dependencies, no memory beyond the current non-terminal. The regular grammar is the generative face of the same structural property that finite automata recognize and regular expressions denote. Its simplicity makes it ideal for specifying lexical tokens and finite-state protocols, though its restricted form also explains why it cannot capture the recursive syntax of programming languages, which require the more permissive productions of context-free grammars.