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Exploring Unrestricted Grammars and Languages in Chomsky Hierarchy

Discover the versatile world of unrestricted grammars, the most powerful form in Chomsky hierarchy. Learn about their components and capabilities with detailed examples. Unleash the complexity and creativity they offer in language generation.

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Exploring Unrestricted Grammars and Languages in Chomsky Hierarchy

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  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

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