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Karp reductions – Definition

SIP 250, AB 42. Karp reductions – Definition. f. Karp Reductions – Ilustrated. B. F(A). A. F( *-A ). * - A. * - B. *. *. Reducing. Reductions and Efficiency. HAMPATH  p HAMCYCLE. u. Check list. Closeness Under Reductions: Definition. Observation. SIP 250, AB 88.

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Karp reductions – Definition

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  1. SIP 250, AB 42 Karp reductions –Definition

  2. f Karp Reductions –Ilustrated B F(A) A F(*-A) * - A * - B * *

  3. Reducing

  4. Reductions and Efficiency

  5. HAMPATHpHAMCYCLE u

  6. Check list

  7. Closeness Under Reductions: Definition

  8. Observation

  9. SIP 250, AB 88 Log-space Reductions

  10. Completeness

  11. Cook reduction

  12. Oracle machines • An oracle Turing machine M has one extra “query tape” and three special states qquery,qyes,qno. • To execute M we specify a language O  {0,1}*, that is used as the “oracle”. • When MO enters qquery, it either moves to qyes or qno according to whether the string on the query tape belongs to O or not. • An oracle call counts as one  step.

  13. Cook reduction - II

  14. Cook reduction: an example • Let L be a language • L* = { x | x=x1..xk , xi L }

  15. Diagonalization yet again

  16. Summary

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