Two incomparable families examined at length are WRB languages generated by normal regular-based W-grammars and WS languages generated by simple W-grammars. Both properly contain the context-free languages and are properly contained in the family of quasirealtime languages. In addition, WRB is closed under nested iterate A mathematical model is presented which embodies salient features of many modern compiling techniques.
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Also, neither B nor C may be the start symbol. Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be efficiently transformed into an equivalent one which is in Chomsky normal form. Furthermore, since all rules deriving nonterminals transform one nonterminal to exactly two nonterminals, a parse tree based on a grammar in Chomsky normal form is a binary tree, and the height of this tree is limited to at most the length of the string. Because of these properties, many proofs in the field of languages and computability make use of the Chomsky normal form.
These properties also yield various efficient algorithms based on grammars in Chomsky normal form; for example, the CYK algorithm that decides whether a given string can be generated by a given grammar uses the Chomsky normal form. Observe that the grammar must be without left recursions.
Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form. Some definitions do not consider the second form of rule to be permitted, in which case a context-free grammar that can generate the null string cannot be so transformed.
This can be used to prove that every context-free language can be accepted by a non-deterministic pushdown automaton. Given a grammar in GNF and a derivable string in the grammar with length n, any top-down parser will halt at depth n.
Greibach normal form is named after Sheila Greibach. Related Questions.
Converting Context Free Grammar to Greibach Normal Form
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