Some properties of precedence languages
Michael J. Fischer · 1969
The classes of languages definable by operator precedence grammars1 and by Wirth-Weber precedence grammars2 are studied. A grammar is backwards-deterministic3 if no two productions have the same right part. Operator precedence grammars have no more generative power than backwards deterministic operator precedence grammars, but Wirth-Weber precedence grammars (i.e., grammars having unique Wirth-Weber precedence relations) are more powerful than backwards-deterministic Wirth-Weber precedence grammars; indeed they can generate any context-free language. An algorithm is developed for finding a Wirth-Weber precedence grammar equivalent to a given operator precedence grammar, a result of possible practical significance. The operator precedence languages are shown to be a proper subclass of the backwards-deterministic Wirth-Weber precedence languages which in turn are a proper subclass of the deterministic context-free languages.