Fred Hennie: Lower Bounds
This chapter discusses attempts over the years to get lower bounds on the NP-complete satisfiability problem. Hennie’s lower bounds for a one-way machine model helped spur still-lively research on time-space tradeoffs for satisfiability.
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Richard J. Lipton r Kenneth W. Regan
People, Problems, and Proofs Essays from Gödel’s Lost Letter: 2010
Richard J. Lipton College of Computing School of Computer Science Georgia Institute of Technology Atlanta, GA, USA
Kenneth W. Regan Dept. of Computer Sci. & Engineering The State University of New York Buffalo, NY, USA
ISBN 978-3-642-41421-3 ISBN 978-3-642-41422-0 (eBook) DOI 10.1007/978-3-642-41422-0 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013956437 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To our dear children: Andrea, Jen, and Rob; Alex and Rebecca
Preface
People, problems, and proofs are the lifeblood of theoretical computer science, which we call theory for short. When you switch on any of the computing devices that have transformed our lives, you are thinking of applications, apps for short. But behind many applications there are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? If so, how? If not, why not? Finally behind these questions are people who are excited by fundamental
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