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The Chomsky Hierarchy

The Chomsky Hierarchy. Linear-Bounded Automata:. Same as Turing Machines with one difference:. the input string tape space is the only tape space allowed to use. Linear Bounded Automaton (LBA). Input string. Working space in tape. Left-end marker. Right-end marker.

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The Chomsky Hierarchy

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  1. The Chomsky Hierarchy Costas Busch - RPI

  2. Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space is the only tape space allowed to use Costas Busch - RPI

  3. Linear Bounded Automaton (LBA) Input string Working space in tape Left-end marker Right-end marker All computation is done between end markers Costas Busch - RPI

  4. We define LBA’s as NonDeterministic Open Problem: NonDeterministic LBA’s have same power as Deterministic LBA’s ? Costas Busch - RPI

  5. Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s have less power than Turing Machines Costas Busch - RPI

  6. Unrestricted Grammars: Productions String of variables and terminals String of variables and terminals Costas Busch - RPI

  7. Example unrestricted grammar: Costas Busch - RPI

  8. Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted grammar Costas Busch - RPI

  9. Context-Sensitive Grammars: Productions String of variables and terminals String of variables and terminals and: Costas Busch - RPI

  10. The language is context-sensitive: Costas Busch - RPI

  11. Theorem: A language is context sensistive if and only if it is accepted by a Linear-Bounded automaton Observation: There is a language which is context-sensitive but not decidable Costas Busch - RPI

  12. The Chomsky Hierarchy Non Turing-Acceptable Turing-Acceptable decidable Context-sensitive Context-free Regular Costas Busch - RPI

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