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The existence of multiple derivations of the same string does not suffice to indicate that the grammar is ambiguous; only multiple leftmost derivations (or, equivalently, multiple parse trees) indicate ambiguity. For example, the simple grammar S → A + A A → 0 | 1 is an unambiguous grammar for the language { 0+0, 0+1, 1+0, 1+1 }.
Ambiguous grammar may result in ambiguous parsing if applied on homographs since the same word sequence can have more than one interpretation. Pun sentences such as the newspaper headline "Iraqi Head Seeks Arms" are an example of ambiguous parses.
Usually, ambiguity is a feature of the grammar, not the language, and an unambiguous grammar can be found that generates the same context-free language. However, there are certain languages that can only be generated by ambiguous grammars; such languages are called inherently ambiguous languages .
This shared forest can conveniently be read as an ambiguous grammar generating only the sentence parsed, but with the same ambiguity as the original grammar, and the same parse trees up to a very simple renaming of non-terminals, as shown by Lang (1994).
A famous example for lexical ambiguity is the following sentence: "Wenn hinter Fliegen Fliegen fliegen, fliegen Fliegen Fliegen hinterher.", meaning "When flies fly behind flies, then flies fly in pursuit of flies." [40] [circular reference] It takes advantage of some German nouns and corresponding verbs being homonymous. While not noticeable ...
The dangling else is a problem in programming of parser generators in which an optional else clause in an if–then(–else) statement can make nested conditional statements ambiguous. Formally, the reference context-free grammar of the language is ambiguous, meaning there is more than one correct parse tree.
The grammar doesn't cover all language rules, such as the size of numbers, or the consistent use of names and their definitions in the context of the whole program. LR parsers use a context-free grammar that deals just with local patterns of symbols. The example grammar used here is a tiny subset of the Java or C language: r0: Goal → Sums eof
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.