1 / 4

Chapter 10

Chapter 10. The Chomsky Hierarchy. Grammars Languages & Accepting Machines. Grammars Languages Accepting Machines Type 3 grammars: Regular DFA Regular grammars , languages NDFA Left-linear grammars, Right-linear grammars

maisie
Download Presentation

Chapter 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 The Chomsky Hierarchy

  2. Grammars Languages & Accepting Machines Grammars Languages Accepting Machines Type 3 grammars: RegularDFA Regular grammars, languagesNDFA Left-linear grammars, Right-linear grammars Type 2 grammars: Context-freePDA Context-free grammarslanguages Type 1 grammars: Contest-sensitive Linear-bounded Context-sensitive grammars, languages Automata Monotonic grammars Type 0 grammars: Recursively DTM Phrase-structure grammars, enumerable, NDTM Unrestricted grammarsUnrestricted

  3. Chapter 10. Unrestricted Grammars • The highest class of the Chomsky hierarchy and the largest class (i.e., most powerful) 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 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   • S: the start symbol

  4. - 1 i Þ *  - 1 i Þ Unrestricted Grammars • Example 10.1.1 The unrestricted grammar V = { S, A, C }  = { a, b, c } P = { S  aAbc |  A  aAbC |  Cb  bC Cc  cc } generates the language { aibici | i  0 } (which is notcontext-free) as S  aAbc aiA(bC)i-1bc  ai(bC)i-1bc  ai(bC)i-2bCbc  ai(bC)i-2bbCc ai(b)i(C)i-1c aibici

More Related