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Summary: A Status Report on the P versus NP Question
Eric Allender
Department of Computer Science
Rutgers University
New Brunswick, NJ 08855, USA
allender@cs.rutgers.edu
Abstract
We survey some of the history of the most famous open question in computing: the P versus NP ques-
tion. We summarize some of the progress that has been made to date, and assess the current situation.
Contents
1 Prologue 2
2 What is the `P=NP?' Problem? 3
2.1 What is an efficient reduction? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Why is this an audacious notion? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Why was this such a big deal? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Complexity Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.5 The class NP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 Subclasses of P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.7 What is the `P=NP?' Problem? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Why is the `P=NP?' Problem Important? 10
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