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Chomsky_Hierarchy

# Chomsky_Hierarchy - → → A language is Turing-Acceptable...

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The Chomsky Hierarchy

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Same as Turing Machines with one difference: the input string tape space is the only tape space allowed to use Linear-Bounded Automata:
[ ] a b c d e Left-end marker Input string Right-end marker Working space  in tape All computation is done between end markers Linear Bounded Automaton (LBA)

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We define LBA’s as NonDeterministic Open Problem: NonDeterministic LBA’s have same power as Deterministic LBA’s ?
Example languages accepted by LBAs: } { n n n c b a L = } { ! n a L = LBA’s have more power than PDA’s                                       (pushdown automata) LBA’s have less power than Turing Machines

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Unrestricted Grammars: Productions v u String of variables and terminals String of variables and terminals
Example unrestricted grammar: d Ac cA aB aBc S

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Unformatted text preview: → → A language is Turing-Acceptable if and only if is generated by an unrestricted grammar L L Theorem: Context-Sensitive Grammars: and: | | | | v u ≤ Productions v u → String of variables and terminals String of variables and terminals The language } { n n n c b a is context-sensitive: aaA aa aB Bb bB Bbcc Ac bA Ab aAbc abc S | | → → → → → A language is context sensistive if and only if it is accepted by a Linear-Bounded automaton L Theorem: There is a language which is context-sensitive but not decidable Observation: Non Turing-Acceptable Turing-Acceptable decidable Context-sensitive Context-free Regular The Chomsky Hierarchy...
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Chomsky_Hierarchy - → → A language is Turing-Acceptable...

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