Time_Complexity

Time_Complexity - TimeComplexity Fall 2006 Costas Busch -...

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Fall 2006 Costas Busch - RPI 1 Time Complexity
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Fall 2006 Costas Busch - RPI 2 M L Consider a deterministic  Turing Machine which decides  a language 
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Fall 2006 Costas Busch - RPI 3 For any string       the computation of terminates in a finite amount of transitions w M      Accept or Reject w Initial state
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Fall 2006 Costas Busch - RPI 4      Accept or Reject w Decision  Time  = #transitions Initial state
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Fall 2006 Costas Busch - RPI 5 Consider now all strings of length n ) (n T M = maximum time required to decide    any string of length  n
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Fall 2006 Costas Busch - RPI 6 ) (n T M Max time to accept a string of length      n 1 2 3 4 n STRING LENGTH TIME
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Fall 2006 Costas Busch - RPI 7 Time Complexity Class: )) ( ( n T TIME All Languages decidable by a deterministic Turing  Machine in time                     1 L 2 L 3 L )) ( ( n T O
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Fall 2006 Costas Busch - RPI 8 Example: } 0 : { 1 = n b a L n This can be decided in           time ) (n O ) (n TIME } 0 : { 1 = n b a L n
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Fall 2006 Costas Busch - RPI 9 ) (n TIME } 0 : { 1 = n b a L n } 0 , : { k n aba ab n } even   is   : { n b n Other example problems in the same class } 3 : { k n b n =
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Time_Complexity - TimeComplexity Fall 2006 Costas Busch -...

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