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Ch10 - variables(i.e non-terminal symbols ∑ the alphabet...

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Chapter 10 The Chomsky Hierarchy
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2 Grammars Languages & Accepting Machines Grammars Languages Accepting Machines Type 3 grammars: Regular FSA Regular grammars , languages NDFA Left-linear grammars, Right-linear grammars Type 2 grammars: Context-free PDA Context-free grammars languages Type 1 grammars: Contest-sensitive Linear-bounded Context-sensitive grammars, languages Automata Monotonic grammars Type 0 grammars: Recursively TM Phrase-structure grammars, enumerable, NDTM Unrestricted grammars Unrestricted
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3 Chapter 10. Unrestricted Grammars The highest class of the Chomsky hierarchy and the largest class of phrase-structured grammars , called type O grammars. Defn.10.1.1 An unrestricted grammar is a quadruple ( V , , P , S ), where V : a finite set of
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Unformatted text preview: variables (i.e., non-terminal symbols) ∑ : the alphabet , a finite set of terminal symbols P : a set of production rules of the form u → v , where u ∈ ( V ∪ ∑ ) + and v ∈ ( V ∪ ∑ )*, i.e., u ≠ λ S : the start symbol 4 Unrestricted Grammars ■ Example 10.1.1 The unrestricted grammar V = { S , A , C } ∑ = { a , b , c } P = { S → aAbc | λ A → aAbC | λ Cb → bC Cc → cc } generates the language { a i b i c i | i ≥ 0 } (which is not context-free) as S ⇒ aAbc a i A ( bC ) i-1 bc ⇒ a i ( bC ) i-1 bc ⇒ a i ( bC ) i-2 bCbc ⇒ a i ( bC ) i-2 bbCc a i ( b ) i ( C ) i-1 c a i b i c i 1-⇒ i ⇒ * 1-⇒ i...
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  • Winter '12
  • DennisNg
  • Formal language, Formal grammar, Context-free grammar, grammars, Chomsky hierarchy, unrestricted grammars

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