Ch10 - variables (i.e., non-terminal symbols) ∑ : the...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 10 The Chomsky Hierarchy
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 03/02/2012 for the course C S 252 taught by Professor Dennisng during the Winter '12 term at BYU.

Page1 / 4

Ch10 - variables (i.e., non-terminal symbols) ∑ : the...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online