Complexity

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Complexity

• CS 611

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Topics for Today

• Ive learned decidability to a level I never
  thought possible.
• Why do I care?
• Thats the topic of paper 2
• 1-2 pages
• Clear up Thm 3.18
• Intro to Complexity
• sup, inf, space bound, off-line, thm 5.1, 5.2

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Why NP-Completeness is useful
Youve been assigned to write an efficient
algorithm for X. After a while, you cant find
an efficient algorithm. Your advisor is getting
restless. Your options are
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Option 2
taken from Garey and Johnson
May lead to undesirable educational outcomes
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Option 3
taken from Garey and Johnson
makes a good paper, if you are right. But the
proof is hard.
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Option 4
taken from Garey and Johnson
easier proof and also a good paper (maybe).
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What NP Completeness is useful to a PhD Student

• The result helps you avoid wasting time coming up
  with an
• efficient and
• correct and
• general purpose algorithm.

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What to do with an NP Complete problem

• Give up.
• Relax the problem.
• Go probabilistic.
• Find efficient solutions to subproblems.
• Buy more hardware.

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Theorems 5.1 and 5.2

• 5.1 If a K-tape TM accepts L in space S(n)
  then a 1-tape TM accepts L in space cS(n).