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Metalanguages have their own metasyntax each composed of terminal symbols, nonterminal symbols, and metasymbols. A terminal symbol, such as a word or a token, is a stand-alone structure in a language being defined. A nonterminal symbol represents a syntactic category, which defines one or more valid phrasal or sentence structure consisted of an ...
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
A derivation rule is composed by a nonterminal symbol and an expression . A special expression α s {\displaystyle \alpha _{s}} is the starting point of the grammar. [ 2 ] In case no α s {\displaystyle \alpha _{s}} is specified, the first expression of the first rule is used.
FIRST(A) is the set of terminals which can appear as the first element of any chain of rules matching nonterminal A. FOLLOW(I) of an Item I [A → α • B β, x] is the set of terminals that can appear immediately after nonterminal B, where α, β are arbitrary symbol strings, and x is an arbitrary lookahead terminal. FOLLOW(k,B) of an item ...
Search the table for the relationship between the nonterminal from the production and first symbol in the stack (Starting from top) Push(Stack, relationship) Push(Stack, Non terminal) SearchProductionToReduce (Stack) Find the topmost ⋖ in the stack; this and all the symbols above it are the Pivot.
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
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.