A Status Report on the P versus NP Question Eric Allender 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 Collections: Computer Technologies and Information Sciences