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Applying the rules recursively to a source string of symbols will usually terminate in a final output string consisting only of terminal symbols. Consider a grammar defined by two rules. In this grammar, the symbol Б is a terminal symbol and Ψ is both a non-terminal symbol and the start symbol. The production rules for creating strings are as ...
Nonterminal symbols are blue and terminal symbols are red. In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form
Similar to a CFG, a probabilistic context-free grammar G can be defined by a quintuple: = (,,,,) where M is the set of non-terminal symbols; T is the set of terminal symbols; R is the set of production rules; S is the start symbol; P is the set of probabilities on production rules
where A, B, and C are nonterminal symbols, the letter a is a terminal symbol (a symbol that represents a constant value), S is the start symbol, and ε denotes the empty string. Also, neither B nor C may be the start symbol, and the third production rule can only appear if ε is in L(G), the language produced by the context-free grammar G.
For readability, the CYK table for P is represented here as a 2-dimensional matrix M containing a set of non-terminal symbols, such that R k is in [,] if, and only if, [,,] . In the above example, since a start symbol S is in M [ 7 , 1 ] {\displaystyle M[7,1]} , the sentence can be generated by the grammar.
An EBNF consists of terminal symbols and non-terminal production rules which are the restrictions governing how terminal symbols can be combined into a valid sequence. Examples of terminal symbols include alphanumeric characters, punctuation marks, and whitespace characters.
is the set of terminal symbols; is the set of productions; is the distinguished, or start, symbol; Then, given a string of nonterminal symbols and an attribute name , . is a synthesized attribute if all three of these conditions are met:
Rewrite rules of a DCPSG are identical to those of a CFG, with the addition of a meta-symbol, denoted here as an underscore. DCPSG rules therefore have the general form X → α {\displaystyle X\to \alpha } where α {\displaystyle \alpha } is a string of terminal symbols and/or non-terminal symbols and at most one underscore.