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Turing Machines (TMs) Linear Bounded Automata (LBAs)

Turing Machines (TMs) Linear Bounded Automata (LBAs). Turing Machine (TM). Input string. Finite State Control Unit. Infinite Tape. Working space in tape. Linear Bounded Automaton (LBA). Input string. Working space in tape. Left-end marker. Right-end marker. Finite State

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Turing Machines (TMs) Linear Bounded Automata (LBAs)

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  1. Turing Machines (TMs)Linear Bounded Automata(LBAs) Costas Busch - RPI

  2. Turing Machine (TM) Input string Finite State Control Unit Infinite Tape Working space in tape Costas Busch - RPI

  3. Linear Bounded Automaton (LBA) Input string Working space in tape Left-end marker Right-end marker Finite State Control Unit 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 with Deterministic LBA’s ? Costas Busch - RPI

  5. Example languages accepted by LBAs: LBA’s have more power than NPDA’s LBA’s have also less power than Turing Machines Costas Busch - RPI

  6. Linear Bounded Automata (LBAs) are the same as Turing Machines with one difference: The input string tape space is the only tape space allowed to use Costas Busch - RPI

  7. The Chomsky Hierarchy Costas Busch - RPI

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

  9. Example unrestricted grammar: Costas Busch - RPI

  10. Theorem: A language is recursively enumerable (r.e.) if and only if is generated by an unrestricted grammar S is r.e. if there exists an algorithm A that enumerates the members of S (A need not necessarily terminate for non-members of S) S is recursive if there exists a decision algorithm that determines if x is a member of S Costas Busch - RPI

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

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

  13. Theorem: A language is context sensitive if and only if is accepted by a Linear-Bounded Automaton Costas Busch - RPI

  14. The Chomsky Hierarchy Non-recursively enumerable Recursively-enumerable Recursive Context-sensitive Context-free Regular Costas Busch - RPI

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