Uniquely inversible grammar

A uniquely inversible grammar is a formal grammar where no two distinct productions give the same result. This implies the specific production can be inferred from its results.

Formal definition

$A \to \alpha \and B \to \beta \iff (A <> B \Rightarrow \alpha <> \beta)$

Examples

Uniquely inversibles

$A \to aA | bB$

$B \to b | a$

Not uniquely inversibles

$A \to aA | bB$

$B \to bB | a$