P = NP

The Golden Ticket: P, NP, and the Search for the Impossible
by Lance Fortnow
Published 30 Mar 2013

Interested parties must apply directly to Random House, Inc. for permission. All Rights Reserved Library of Congress Cataloging-in-Publication Data Fortnow, Lance, 1963– The golden ticket : P, NP, and the search for the impossible / Lance Fortnow. pages cm Summary: “The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology.

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The most prestigious computer science journal receives a steady stream of papers claiming to resolve the P versus NP question and has a specific policy for those papers: The Journal of the ACM frequently receives submissions purporting to solve a long-standing open problem in complexity theory, such as the P/NP problem. Such submissions tax the voluntary editorial and peer-reviewing resources used by JACM, by requiring the review process to identify the errors in them. JACM remains open to the possibility of eventual resolution of P/NP and related questions, and continues to welcome submissions on the subject. However, to mitigate the burden of repeated resubmissions of incremental corrections of errors identified during editorial review, JACM has adopted the following policy: No author may submit more than one paper on the P/NP or related long-standing questions in complexity theory in any 24 month period, except by invitation of the Editor-in-Chief.

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In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem”—Provided by publisher. Includes bibliographical references and index. ISBN 978-0-691-15649-1 (hardback) 1.

The Simpsons and Their Mathematical Secrets
by Simon Singh
Published 29 Oct 2013

Algorithms to Live By: The Computer Science of Human Decisions
by Brian Christian and Tom Griffiths
Published 4 Apr 2016

The intractable scheduling problems that Eugene Lawler encountered in chapter 5 fall into this category. An NP-hard problem that is itself in NP is known as “NP-complete.” See Karp, “Reducibility Among Combinatorial Problems,” for the classic result showing that a version of the traveling salesman problem is NP-complete, and Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible, for an accessible introduction to P and NP. most computer scientists believe that there aren’t any: In a 2002 survey of one hundred leading theoretical computer scientists, sixty-one thought P ≠ NP and only nine thought P = NP (Gasarch, “The P =? NP Poll”). While proving P = NP could be done by exhibiting a polynomial-time algorithm for an NP-complete problem, proving P ≠ NP requires making complex arguments about the limits of polynomial-time algorithms, and there wasn’t much agreement among the people surveyed about exactly what kind of mathematics will be needed to solve this problem.

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______. “The Traveling-Salesman Problem.” Operations Research 4, no. 1 (1956): 61–75. ______. “What Future Is There for Intelligent Machines?” Audio Visual Communication Review 11, no. 6 (1963): 260–270. Forster, Edward M. Howards End. London: Edward Arnold, 1910. Fortnow, Lance. The Golden Ticket: P, NP, and the Search for the Impossible. Princeton, NJ: Princeton University Press, 2013. Fraker, Guy C. “The Real Lincoln Highway: The Forgotten Lincoln Circuit Markers.” Journal of the Abraham Lincoln Association 25 (2004): 76–97. Frank, Robert H. “If Homo Economicus Could Choose His Own Utility Function, Would He Want One with a Conscience?”

The Half-Life of Facts: Why Everything We Know Has an Expiration Date
by Samuel Arbesman
Published 31 Aug 2012

The Road to Conscious Machines
by Michael Wooldridge
Published 2 Nov 2018

Natural language processing with Python
by Steven Bird , Ewan Klein and Edward Loper
Published 15 Dec 2009

To begin with, we construct a list of bigrams whose members are themselves word-tag pairs, such as (('The', 'DET'), ('Fulton', 'NP')) and (('Fulton', 'NP'), ('County', 'N')). Then we construct a FreqDist from the tag parts of the bigrams. >>> word_tag_pairs = nltk.bigrams(brown_news_tagged) >>> list(nltk.FreqDist(a[1] for (a, b) in word_tag_pairs if b[1] == 'N')) ['DET', 'ADJ', 'N', 'P', 'NP', 'NUM', 'V', 'PRO', 'CNJ', '.', ',', 'VG', 'VN', ...] This confirms our assertion that nouns occur after determiners and adjectives, including numeral adjectives (tagged as NUM). Verbs Verbs are words that describe events and actions, e.g., fall and eat, as shown in Table 5-3. In the context of a sentence, verbs typically express a relation involving the referents of one or more noun phrases.

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Ubiquitous Ambiguity A well-known example of ambiguity is shown in (2), from the Groucho Marx movie, Animal Crackers (1930): (2) While hunting in Africa, I shot an elephant in my pajamas. How an elephant got into my pajamas I’ll never know. Let’s take a closer look at the ambiguity in the phrase: I shot an elephant in my pajamas. First we need to define a simple grammar: >>> ... ... ... ... ... ... ... ... ... groucho_grammar = nltk.parse_cfg(""" S -> NP VP PP -> P NP NP -> Det N | Det N PP | 'I' VP -> V NP | VP PP Det -> 'an' | 'my' N -> 'elephant' | 'pajamas' V -> 'shot' P -> 'in' """) 8.1 Some Grammatical Dilemmas | 293 This grammar permits the sentence to be analyzed in two ways, depending on whether the prepositional phrase in my pajamas describes the elephant or the shooting event. >>> sent = ['I', 'shot', 'an', 'elephant', 'in', 'my', 'pajamas'] >>> parser = nltk.ChartParser(groucho_grammar) >>> trees = parser.nbest_parse(sent) >>> for tree in trees: ... print tree (S (NP I) (VP (V shot) (NP (Det an) (N elephant) (PP (P in) (NP (Det my) (N pajamas)))))) (S (NP I) (VP (VP (V shot) (NP (Det an) (N elephant))) (PP (P in) (NP (Det my) (N pajamas))))) The program produces two bracketed structures, which we can depict as trees, as shown in (3): (3) a.

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By convention, the lefthand side of the first production is the start-symbol of the grammar, typically S, and all well-formed trees must have this symbol as their root label. In NLTK, contextfree grammars are defined in the nltk.grammar module. In Example 8-1 we define a grammar and show how to parse a simple sentence admitted by the grammar. Example 8-1. A simple context-free grammar. grammar1 = nltk.parse_cfg(""" S -> NP VP VP -> V NP | V NP PP PP -> P NP V -> "saw" | "ate" | "walked" NP -> "John" | "Mary" | "Bob" | Det N | Det N PP Det -> "a" | "an" | "the" | "my" N -> "man" | "dog" | "cat" | "telescope" | "park" P -> "in" | "on" | "by" | "with" """) >>> sent = "Mary saw Bob".split() >>> rd_parser = nltk.RecursiveDescentParser(grammar1) >>> for tree in rd_parser.nbest_parse(sent): ... print tree (S (NP Mary) (VP (V saw) (NP Bob))) The grammar in Example 8-1 contains productions involving various syntactic categories, as laid out in Table 8-1.

Algorithms Unlocked
by Thomas H. Cormen
Published 15 Jan 2013

Too Big to Know: Rethinking Knowledge Now That the Facts Aren't the Facts, Experts Are Everywhere, and the Smartest Person in the Room Is the Room
by David Weinberger
Published 14 Jul 2011

Indeed, the space within which credentialed science occurs is becoming dramatically and usefully more entwined with the rest of its environment. For example, on August 6, 2010, the mathematician Vinay Deolalikar sent to his colleagues a manuscript proposing a solution to a mathematical problem so notoriously difficult that there’s a million-dollar prize for solving it.34 The “P≠NP” problem had previously brought down some seriously brilliant mathematicians who thought they had it licked. This time, however, the person who originally formulated the problem emailed Deolalikar’s solution to some of his colleagues, saying, “This appears to be a relatively serious claim to have solved P vs.

Elliptic Tales: Curves, Counting, and Number Theory
by Avner Ash and Robert Gross
Published 12 Mar 2012

The set E(Fp )ns is still nonempty, and is in fact also an abelian group, just as E(Fp ) was for good p, as we saw in chapter 9. We let Np stand for the number of points in E(Fp )ns . For the good primes p, E modulo p is nonsingular, so Np is simply the number of points in E(Fp ). For the bad primes p, we worked out Np in chapter 9. The results, taken from table 9.4, are that Np = p if E has additive reduction at p, Np = p − 1 if E has split multiplicative reduction at p, and Np = p + 1 if E has nonsplit multiplicative reduction at p. Next we review the definition of the integer ap , defined for every prime p . If E modulo p is nonsingular (good p), we set Np = p + 1 − ap . 208 CHAPTER 13 If E modulo p is singular (bad p), we set Np = p − ap , where we took away 1 because E(Fp ) has one singular point that we are not counting.

Quantum Computing for Everyone
by Chris Bernhardt
Published 19 Mar 2019

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
by Pedro Domingos
Published 21 Sep 2015

Average Is Over: Powering America Beyond the Age of the Great Stagnation
by Tyler Cowen
Published 11 Sep 2013

Applied Cryptography: Protocols, Algorithms, and Source Code in C
by Bruce Schneier
Published 10 Nov 1993

Brassard, “Quantum Public Key Distribution Reinvented,” SIGACT News, v. 18, n. 4, 1987, pp. 51–53. 127. C.H. Bennett and G. Brassard, “The Dawn of a New Era for Quantum Cryptography: The Experimental Prototype is Working!” SIGACT News, v. 20, n. 4, Fall 1989, pp. 78–82. 128. C.H. Bennett, G. Brassard, and S. Breidbart, Quantum Cryptography II: How to Re–Use a One–Time Pad Safely Even if P=NP, unpublished manuscript, Nov 1982. 129. C.H. Bennett, G. Brassard, S. Breidbart, and S. Weisner, “Quantum Cryptography, or Unforgeable Subway Tokens,” Advances in Cryptology: Proceedings of Crypto 82, Plenum Press, 1983, pp. 267–275. 130. C.H. Bennett, G. Brassard, C. Crépeau, and M.–H. Skubiszewska, “Practical Quantum Oblivious Transfer,” Advances in Cryptology—CRYPTO ’91 Proceedings, Springer–Verlag, 1992, pp. 351–366. 131.

Journey to the Edge of Reason: The Life of Kurt Gödel
by Stephen Budiansky
Published 10 May 2021

The End of Money: Counterfeiters, Preachers, Techies, Dreamers--And the Coming Cashless Society
by David Wolman
Published 14 Feb 2012

Hands-On Machine Learning With Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems
by Aurelien Geron
Published 14 Aug 2019

The Music of the Primes
by Marcus Du Sautoy
Published 26 Apr 2004

The Haskell Road to Logic, Maths and Programming
by Kees Doets , Jan van Eijck and Jan Eijck
Published 15 Jan 2004

Syntactic Structures
by Noam Chomsky
Published 17 Oct 2008

Asset and Risk Management: Risk Oriented Finance
by Louis Esch , Robert Kieffer and Thierry Lopez
Published 28 Nov 2005

How I Became a Quant: Insights From 25 of Wall Street's Elite
by Richard R. Lindsey and Barry Schachter
Published 30 Jun 2007

Hands-On Machine Learning With Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems
by Aurélien Géron
Published 13 Mar 2017

Peer-to-Peer
by Andy Oram
Published 26 Feb 2001

In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation
by William J. Cook
Published 1 Jan 2011

In Pursuit of Privilege: A History of New York City's Upper Class and the Making of a Metropolis
by Clifton Hood
Published 1 Nov 2016

Python for Finance
by Yuxing Yan
Published 24 Apr 2014

In the following program, we have three input values: ticker, begdate (first date), and enddate (second date): import datetime import matplotlib.pyplot as plt from matplotlib.finance import quotes_historical_yahoo from matplotlib.dates import MonthLocator,DateFormatter ticker='AAPL' begdate= datetime.date( 2012, 1, 2 ) enddate = datetime.date( 2013, 12,4) months = MonthLocator(range(1,13), bymonthday=1, interval=3) # every 3rd month monthsFmt = DateFormatter("%b '%Y") x = quotes_historical_yahoo(ticker, begdate, enddate) if len(x) == 0: print ('Found no quotes') raise SystemExit dates = [q[0] for q in x] closes = [q[4] for q in x] fig, ax = plt.subplots() ax.plot_date(dates, closes, '-') ax.xaxis.set_major_locator(months) ax.xaxis.set_major_formatter(monthsFmt) ax.xaxis.set_minor_locator(mondays) ax.autoscale_view() ax.grid(True) fig.autofmt_xdate() [ 153 ] Visual Finance via Matplotlib The output graph is shown as follows: IBM's intra-day graphical representations We could demonstrate the price movement of a stock for a given period, for example, from January 2009 to today. First, let's look at the intra-day price pattern. The following program will be explained in the next chapter: import pandas as pd, numpy as np, datetime ticker='AAPL' path='http://www.google.com/finance/getprices?q=ttt&i=60&p=1d&f=d,o,h,l,c ,v' p=np.array(pd.read_csv(path.replace('ttt',ticker),skiprows=7,header=No ne)) date=[] for i in arange(0,len(p)): if p[i][0][0]=='a': t= datetime.datetime.fromtimestamp(int(p[i][0].replace('a',''))) date.append(t) else: date.append(t+datetime.timedelta(minutes =int(p[i][0]))) [ 154 ] Chapter 7 final=pd.DataFrame(p,index=date) final.columns=['a','Open','High','Low','Close','Vol'] del final['a'] x=final.index y=final.Close title('Intraday price pattern for ttt'.replace('ttt',ticker)) xlabel('Price of stock') ylabel('Intro-day price pattern') plot(x,y) show() The graph is shown in the following image: [ 155 ] Visual Finance via Matplotlib A more complex program that we can run to find the intra-day pattern could be found at http://matplotlib.org/examples/pylab_examples/finance_work2. html.

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In addition, sometimes we have to convert daily returns to weekly or monthly, or convert monthly returns to quarterly or annual. Thus, understanding how to estimate returns and their conversion is vital. Assume that we have four prices and we choose the first and last three prices as follows: >>>import numpy as np >>>p=np.array([1,1.1,0.9,1.05]) [ 185 ] Statistical Analysis of Time Series It is important how these prices are sorted. If the first price happened before the second price, we know that the first return should be (1.1-1)/1=10%. Next, we learn how to retrieve the first n-1 and the last n-1 records from an n-record array.

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This correlation is represented in the following code: import numpy as np import statsmodels.api as sm from matplotlib.finance import quotes_historical_yahoo begdate=(2013,10,1) enddate=(2013,10,30) ticker='IBM' #WMT data= quotes_historical_yahoo(ticker, begdate, enddate,asobject=True, adjusted=True) p=np.array(data.aclose) dollar_vol=np.array(data.volume*p) ret=np.array((p[1:] - p[:-1])/p[1:]) illiq=mean(np.divide(abs(ret),dollar_vol[1:])) print("Aminud illiq=", illiq) ('Aminud illiq=', 1.1650681670001537e-11) Pastor and Stambaugh (2003) liquidity measure Based on the methodology and empirical evidence in Campbell, Grossman, and Wang (1993), Pastor and Stambaugh (2003) designed the following model to measure individual stock's liquidity and the market liquidity: \W D  E [W   E  [W   W (9) Here, yt is the excess stock return, 5W  5 I W , on day t, 5W is the return for the stock, 5 I W is the risk-free rate, [W is the market return; [W is the signed dollar trading volume ( x2,t = sign Rt − R f ,t ∗ pt ∗ volumet), pt is the stock price, and YROXPHW is the trading volume.

Reinventing Discovery: The New Era of Networked Science
by Michael Nielsen
Published 2 Oct 2011

Advances in Financial Machine Learning
by Marcos Lopez de Prado
Published 2 Feb 2018

Human Compatible: Artificial Intelligence and the Problem of Control
by Stuart Russell
Published 7 Oct 2019

Artificial Intelligence: A Modern Approach
by Stuart Russell and Peter Norvig
Published 14 Jul 2019

The Wrecking Crew: How Conservatives Rule
by Thomas Frank
Published 5 Aug 2008

.: Conservative Caucus, 1983), p. 181. 27. The word “revolution” could even take on the wistful notes of lost youth, as at a 1992 College Republican reunion when Abramoff, by then a producer of wretched movies, hosted an alumni session called “Rejoin the Revolution.” See 1992 College Republicans’ Centennial Celebration (n.p.: n.p., n.d. [1992]). Sword and shield: “Message from the Chairman” in the 1983 Annual Report of the College Republicans, p. 3. The phrase is also used in the 1982 Review of the NEWS interview cited above and in a 1995 profile by John W. Moore, “A Lobbyist With a Line to Capitol Hill,” National Journal, July 29, 1995.

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Since the breaking of the Abramoff scandal, however, Waller has become a frequent critic of the fallen lobbyist, recounting for other journalists how Abramoff played Washington’s right-wing network for his various lobbying clients. (He did not respond to inquiries from me.) “Deputy projects director”: College Republican National Committee, Forty-Fifth Biennial Convention (n.p.: n.p., 1983), n.p. YAF magazine: J. Michael Waller, “Bare-Fisted Journalism,” New Guard, Winter 1982–83, p. 37. Crashing the IPS party: CR Report, May 14, 1983, p. 2. USA Foundation: J. Michael Waller, “CISPES: A Guerrilla Propaganda Network,” a twenty-one-page report printed on United Students of America Foundation letterhead, with a cover letter signed by Jack Abramoff and dated November 7, 1983, from collections of Political Research Associates.

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“CNMI policy permits the staffing of major employers in the territory—garment factories, security companies, the hotel industry—with a permanent floating army of foreign workers who have no opportunity to become permanent members of the community and who, by nature of their status, culture and powerlessness, are extremely vulnerable to exploitation, pressure, and mistreatment.” Congressman George Miller and Democratic Staff of the House Committee on Resources, “Beneath the American Flag: Labor and Human Rights Abuses in the CNMI” (n.p.: n.p., March 26, 1998), p. 15. 9. “The fact that an employer can have an alien worker removed from the CNMI on one-day’s notice is a powerful incentive for an alien to obey an employer’s demands, even though the demands may be illegal or abusive.” Third Annual Report, p. 11. 10. As of 1997, the minimum wage in Saipan for garment and construction workers was $2.90 per hour; for more exalted occupations it was $3.05 per hour.

The Man From the Future: The Visionary Life of John Von Neumann
by Ananyo Bhattacharya
Published 6 Oct 2021

Macrae, John von Neumann. 102. ‘Benoît Mandelbrot – Post-doctoral Studies: Weiner and Von Neumann (36/144)’, Web of Stories – Life Stories of Remarkable People, https://www.youtube.com/watch?v=U9kw6Reml6s. 103. https://rjlipton.wpcomstaging.com/the-gdel-letter/. Also see Richard J. Lipton, 2010, The P=NP Question and Gödel’s Lost Letter, Springer, New York. 104. John von Neumann to Marina von Neumann, 19 April 1955, quoted in von Neumann Whitman, The Martian’s Daughter. 105. Quoted in Dyson, Turing’s Cathedral. 106. Quoted in ibid. 107. Email to author. 108. John von Neumann, Documentary Mathematical Association of America, 1966. 109.

Higher-Order Perl: A Guide to Program Transformation
by Mark Jason Dominus
Published 14 Mar 2005

The Art of Computer Programming
by Donald Ervin Knuth
Published 15 Jan 2001

The Art of Assembly Language
by Randall Hyde
Published 8 Sep 2003

Global Catastrophic Risks
by Nick Bostrom and Milan M. Cirkovic
Published 2 Jul 2008

Rationality: From AI to Zombies
by Eliezer Yudkowsky
Published 11 Mar 2015