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Indexed Grammar
Indexed grammars are a generalization of context-free grammars in that nonterminals are equipped with lists of ''flags'', or ''index symbols''. The language produced by an indexed grammar is called an indexed language. Definition Modern definition by Hopcroft and Ullman In contemporary publications following Hopcroft and Ullman (1979), an indexed grammar is formally defined a 5-tuple ''G'' = ⟨''N'',''T'',''F'',''P'',''S''⟩ where * ''N'' is a set of variables or Nonterminal, nonterminal symbols, * ''T'' is a set ("alphabet (formal languages), alphabet") of terminal symbols, * ''F'' is a set of so-called ''index symbols'', or ''indices'', * ''S'' ∈ ''N'' is the ''start symbol (formal languages), start symbol'', and * ''P'' is a finite set of ''Production (formal languages), productions''. In productions as well as in derivations of indexed grammars, a string ("stack") ''σ'' ∈ ''F''Kleene star, * of index symbols is attached to every nonterminal symbol ''A'' ∈ ''N'', de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). A formal grammar is "context-free" if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. This is what distinguishes it from a context-sensitive grammar. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, :\langle\text\rangle \to \langle\text\rangle = \langle\text\rangle ; replaces \langle\text\rangle with \langle\text\rangle = \langle\text\rangle ;. There can be multiple replacement rules for a given nonterminal symbol. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
