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Linear Bounded Automata: From Context-Sensitive to Turing-Acceptable

Learn about Costas Busch's research on linear bounded automata, their power compared to PDA and Turing machines, and the Chomsky Hierarchy. Explore examples of LBAs and unrestricted grammars. Discover the theorems linking languages to automata complexity.

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Linear Bounded Automata: From Context-Sensitive to Turing-Acceptable

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  1. The Chomsky Hierarchy Costas 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 Costas 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 Costas Busch - LSU

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

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

  7. Example unrestricted grammar: Costas Busch - LSU

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

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

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

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

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