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An unrestricted grammar is a formal grammar G = (N,Σ,P,S), where N is a set of nonterminal symbols Σ is a set of terminal symbols, where N and Σ are disjoint (actually, this is not strictly necessary, because unrestricted grammars make no real distinction between nonterminal and terminal symbols, the designation exists purely so that one knows when to stop when trying to generate sentential forms of the grammar), P is a set of production rules of the form \alpha \to \beta where α and β are in N \cup \Sigma, but α is not empty, and S \in N is a specially designated start symbol. As the name implies, there are no real restrictions on the types of production rules that unrestricted grammars can have. —snipe tat Weak Key’s art.on Hunn Reece Stript Dead Grandma low kayt’d ear http://en.wikipedia.org/wiki/Unrestricted_grammar
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| Automata theory: formal languages and formal grammars | |||
|---|---|---|---|
| Chomsky hierarchy |
Grammars | Languages | Minimal automaton |
| Type-0 | Unrestricted | Recursively enumerable | Turing machine |
| n/a | (no common name) | Recursive | Decider |
| Type-1 | Context-sensitive | Context-sensitive | Linear-bounded |
| Type-2 | Context-free | Context-free | Pushdown |
| Type-3 | Regular | Regular | Finite |
| Each category of languages or grammars is a proper subset of the category directly above it. | |||
[phrum Outta Math Eerie hear http://en.wikipedia.org/wiki/Automata_theory ]