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Context-free grammars are a special form of Semi-Thue systems that in their general form date back to the work of Axel Thue. The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, [3] and also their classification as a special type of formal grammar (which he called phrase-structure grammars). [4]
A weighted context-free grammar (WCFG) is a more general category of context-free grammar, where each production has a numeric weight associated with it. The weight of a specific parse tree in a WCFG is the product [7] (or sum [8]) of all rule weights in the tree. Each rule weight is included as often as the rule is used in the tree.
Determining if a context-free grammar generates all possible strings, or if it is ambiguous. Given two context-free grammars, determining whether they generate the same set of strings, or whether one generates a subset of the strings generated by the other, or whether there is any string at all that both generate.
To convert a grammar to Chomsky normal form, a sequence of simple transformations is applied in a certain order; this is described in most textbooks on automata theory. [4]: 87–94 [5] [6] [7] The presentation here follows Hopcroft, Ullman (1979), but is adapted to use the transformation names from Lange, Leiß (2009).
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. [ 1 ] [ 2 ] Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule.
The Earley parser executes in cubic time in the general case (), where n is the length of the parsed string, quadratic time for unambiguous grammars (), [4] and linear time for all deterministic context-free grammars. It performs particularly well when the rules are written left-recursively.
Some do not permit the second form of rule and cannot transform context-free grammars that can generate the empty word. For one such construction the size of the constructed grammar is O( n 4 ) in the general case and O( n 3 ) if no derivation of the original grammar consists of a single nonterminal symbol, where n is the size of the original ...
A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser. [1] The concept was first created in 1964 by Claude Pair, [2] and was later rediscovered, from ideas due to Robert Floyd, by Niklaus Wirth and Helmut Weber who published a paper, entitled EULER: a generalization of ALGOL, and its formal definition, published in 1966 in the ...
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