Randomized Algorithms (Spring 2010)/Fingerprinting: Difference between revisions

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==== Example: Checking matrix multiplication ====
==== Example: Checking matrix multiplication ====
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:Input
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*'''Input''': Three <math>n\times n</math> matrices <math>A,B</math> and <math>C</math>.
 
*'''Question''': Is <math>C=AB</math>?
|}
|}



Revision as of 12:42, 2 June 2010

Fingerprinting

Evaluating at random points

Example: Checking matrix multiplication

  • Input: Three [math]\displaystyle{ n\times n }[/math] matrices [math]\displaystyle{ A,B }[/math] and [math]\displaystyle{ C }[/math].
  • Question: Is [math]\displaystyle{ C=AB }[/math]?

Example: Checking polynomial identities

Evaluating over a random field

Example: Identity checking

Example: Randomized pattern matching

Universal hashing

Example: checking distinctness

Probabilistic Checkable Proofs (PCPs)