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Deterministic context-free languages are commonly defined using an automaton concept, the (restricted, deterministic) pushdown automaton. To some that is confusing, as the name context-free refers to a grammar type.

I seem to remember there exists a characterization of the DCF languages using grammars. In my recollection it used a complicated equivalence on non-terminals. Can anyone provide a pointer to that work?

Raphael
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Hendrik Jan
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2 Answers2

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Wikipedia actually gives you the model and points to [1] for reference: LR grammars are equivalent to DPDA.

  1. On the Translation of Languages from Left to Right by Donald Knuth (1965) [free download]
Raphael
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  • Thanks. This helped me to re-investigate. The class I was looking for is called strict deterministic grammars (Harrison & Havel, JCSS 1973) and characterizes the prefix-free deterministic context-free languages. Not all of them. The good side if the class is that is defined on the productions, not on the derivations, like LR-grammars do. Adding an end-marker mekes every language prefix-free, so in practical terms that is not a big loss. Note wikipedia has the notion, hidden under "Strict determinism". (Can I do links in a comment?) – Hendrik Jan Nov 30 '12 at 21:02
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Just an additional note of possible use: the PLL(0) grammars == the strict deterministic grammars, perhaps an easier approach for both understanding and practical application. A nice description is in Parsing Techniques, 2nd Edition, pp354-357.

Ron Burk
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