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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 Prof. Busch - LSU

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

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

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

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

  6. Unrestricted Grammars: Productions String of variables and terminals String of variables and terminals Prof. Busch - LSU

  7. Example unrestricted grammar: Prof. Busch - LSU

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

  9. Context-Sensitive Grammars: Productions String of variables and terminals String of variables and terminals and: Prof. Busch - LSU

  10. The language is context-sensitive: Prof. Busch - LSU

  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 Prof. Busch - LSU

  12. The Chomsky Hierarchy Non Turing-Acceptable Turing-Acceptable decidable Context-sensitive Context-free Regular Prof. Busch - LSU

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