CS355

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CS355 The Mathematics and Theory of Computer
Science

• Reducibility

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Reductions

• A reduction is a way of converting one problem to
  another problem in such a way that a solution to
  the second one can be used to solve the first
  problem.
• Such reducibilities occur in every day life, even
  if we dont call them reductions.
• E.g. Imagine you are lost in a city. You could
  reduce the problem of finding your way to the
  problem of obtaining a map of the city.

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Reductions

• Reducibility also occurs in mathematical
  problems.
• The problem of getting the circumference of a
  rectangle reduced to the problem of finding its
  length and width.
• Reducibility plays an important role in
  classifying problems by decidability and also in
  complexity theory.

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Reductions

• When A is reducible to B, solving A cannot be
  harder than solving B because a solution to B
  gives a solution to A.
• Let us look at a problem HALTTM the problem of
  determining whether a TM halts (by accepting or
  rejecting) a given input.