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KOLMOGOROV COMPLEXITY Kolmogorov Complexity Lance Fortnow 1. Introduction 010101010101010101010101 100111011101011100100110 110100110010110100101100 Consider the three strings shown above.MORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
A COMPUTATIONAL THEORY OF AWARENESS AND DECISION MAKING A Computational Theory of Awareness and Decision Making Nikhil R Devanur Microsoft Research One Microsoft way Redmond, WA Lance Fortnowy Department of EECSONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, and AC - LANCE.FORTNOW.COM Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e er LANCE FORTNOWPRESENTATIONSBIOGRAPHYRIBBITCOMPUTER OTHELLO PROGRAMSTUDENTSPUBLICATIONS Lance Fortnow. Dean of the College of Computing. Illinois Institute of Technology Email: lfortnow@iit.edu. Office: IIT Tower, 14th Floor, Room 14F9-1. Phone: (847) 579-9310. LANCE FORTNOW PUBLICATIONS Publications. Important Notes: The copyrights for journal and conference proceedings papers generally belong to the publisher of the journal or proceedings. All papers may be downloaded for personal or research purposes only. The PDF files are the most recent versions of each paper and may not correspond to the referenced version. LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University of THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE IMPOSSIBLE 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 COMPRESSION COMPLEXITY Compression Complexity Stephen Fenner University of South Carolina Lance Fortnow Georgia Institute of Technology February 15, 2017 Abstract The Kolmogorov complexity of x, denoted C(x), is the lengthof
KOLMOGOROV COMPLEXITY Kolmogorov Complexity Lance Fortnow 1. Introduction 010101010101010101010101 100111011101011100100110 110100110010110100101100 Consider the three strings shown above.MORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
A COMPUTATIONAL THEORY OF AWARENESS AND DECISION MAKING A Computational Theory of Awareness and Decision Making Nikhil R Devanur Microsoft Research One Microsoft way Redmond, WA Lance Fortnowy Department of EECSONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, and AC - LANCE.FORTNOW.COM Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e er LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University ofONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, and INVERTING ONTO FUNCTIONS Inverting Onto Functions Stephen A. Fenner1 University of Southern Maine Portland, ME 04103 Email: fenner@cse.sc.edu and Lance Fortnow2 and Ashish V. Naik3 University of Chicago OPTIMAL - LANCE FORTNOW W e sa y a set A reduces to B if there exists p olynomial-time computable function f suc h that for all strings x, is in A if and only B. W e also call this an m-reduction, \m" forPRESENTS RIBB IT
INSTRUCTIONS 1. Boot the Ribbit diskette and follow the directions in order to play. On the screen you will see: P-Play D-Demo Press the "P" key and you may play the game.TURING’S DOTS
Turing’s Dots Lance Fortnow Northwestern University Abstract Discussion of Turing’s paper \The Use of Dots as Brackets in Church’s Sys-tem," J. Symbolic Logic 7, pp 146-156 (1942) LOW-DEPTH WITNESSES ARE EASY TO FIND Low-Depth Witnesses are Easy to Find 3 of accepting paths for each input. 2.1. Kolmogorov Complexity. For a full understanding of Kolmogorov complexity we refer the reader to the book of Li & Vit anyi(2008).
TESTING CLOSENESS OF DISCRETE DISTRIBUTIONS Testing Closeness of Discrete Distributions · 3 sublinearin the size ofthe Markovchainfor smallt. We then investigatetwonotions of being close to a rapidly mixing Markov chain that fall within the framework of property testing, and show how to test that a given Markov chain isclose to a
TIME FOR COMPUTER SCIENCE TO GROW UP Time for Computer Science to Grow Up Lance Fortnow Northwestern University Abstract Unlike every other academic eld, Computer Scienceuses conferences
ALGEBRAIC METHO DS FOR IN TERACTIV E PRO OF SYSTEMS IP of languages accepted b y in teractiv e pro of systems w as not m uc h larger than NP. In particular, it w as b eliev ed that co-NP-complete languages did not ha LANCE FORTNOWPRESENTATIONSBIOGRAPHYRIBBITCOMPUTER OTHELLO PROGRAMSTUDENTSPUBLICATIONS Lance Fortnow. Dean of the College of Computing. Illinois Institute of Technology Email: lfortnow@iit.edu. Office: IIT Tower, 14th Floor, Room 14F9-1. Phone: (847) 579-9310. LANCE FORTNOW PUBLICATIONS Publications. Important Notes: The copyrights for journal and conference proceedings papers generally belong to the publisher of the journal or proceedings. All papers may be downloaded for personal or research purposes only. The PDF files are the most recent versions of each paper and may not correspond to the referenced version. LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University of THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE IMPOSSIBLE 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 COMPRESSION COMPLEXITY Compression Complexity Stephen Fenner University of South Carolina Lance Fortnow Georgia Institute of Technology February 15, 2017 Abstract The Kolmogorov complexity of x, denoted C(x), is the lengthof
MORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
INVERTING ONTO FUNCTIONS Inverting Onto Functions Stephen A. Fenner1 University of Southern Maine Portland, ME 04103 Email: fenner@cse.sc.edu and Lance Fortnow2 and Ashish V. Naik3 University of Chicago KOLMOGOROV COMPLEXITY Kolmogorov Complexity Lance Fortnow 1. Introduction 010101010101010101010101 100111011101011100100110 110100110010110100101100 Consider the three strings shown above.AC - LANCE FORTNOW
Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e erONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, and LANCE FORTNOWPRESENTATIONSBIOGRAPHYRIBBITCOMPUTER OTHELLO PROGRAMSTUDENTSPUBLICATIONS Lance Fortnow. Dean of the College of Computing. Illinois Institute of Technology Email: lfortnow@iit.edu. Office: IIT Tower, 14th Floor, Room 14F9-1. Phone: (847) 579-9310. LANCE FORTNOW PUBLICATIONS Publications. Important Notes: The copyrights for journal and conference proceedings papers generally belong to the publisher of the journal or proceedings. All papers may be downloaded for personal or research purposes only. The PDF files are the most recent versions of each paper and may not correspond to the referenced version. LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University of THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE IMPOSSIBLE 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 COMPRESSION COMPLEXITY Compression Complexity Stephen Fenner University of South Carolina Lance Fortnow Georgia Institute of Technology February 15, 2017 Abstract The Kolmogorov complexity of x, denoted C(x), is the lengthof
MORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
INVERTING ONTO FUNCTIONS Inverting Onto Functions Stephen A. Fenner1 University of Southern Maine Portland, ME 04103 Email: fenner@cse.sc.edu and Lance Fortnow2 and Ashish V. Naik3 University of Chicago KOLMOGOROV COMPLEXITY Kolmogorov Complexity Lance Fortnow 1. Introduction 010101010101010101010101 100111011101011100100110 110100110010110100101100 Consider the three strings shown above.AC - LANCE FORTNOW
Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e erONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, andFORTNOW FAMILY
The Fortnow Family. Lance Matt Molly Marcy Annie Matt Molly MarcyAnnie
LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University of INVERTING ONTO FUNCTIONS Inverting Onto Functions Stephen A. Fenner1 University of Southern Maine Portland, ME 04103 Email: fenner@cse.sc.edu and Lance Fortnow2 and Ashish V. Naik3 University of ChicagoTURING’S DOTS
Turing’s Dots Lance Fortnow Northwestern University Abstract Discussion of Turing’s paper \The Use of Dots as Brackets in Church’s Sys-tem," J. Symbolic Logic 7, pp 146-156 (1942)ONE-SIDED - FORTNOW
De niti on 4. W e say that a language A is RP-c onsistent with a pr ob abilistic p olynomial-time T uring machine M if for al l x 2, x is in A if Pr (M ac c epts) 1 = 2, and LEARNING REDUCTIONS TO SPARSE SETS The least common notation we use, is: PNP k and FP NP, which are the classes of sets and functions, respectively, that are polynomial-time computable with non-adaptive queries to an NP oracle; PNP, and FPNP, the classes of sets and functions that are polynomial-timecomputable by
PRESENTS RIBB IT
INSTRUCTIONS 1. Boot the Ribbit diskette and follow the directions in order to play. On the screen you will see: P-Play D-Demo Press the "P" key and you may play the game. TESTING CLOSENESS OF DISCRETE DISTRIBUTIONS Testing Closeness of Discrete Distributions · 3 sublinearin the size ofthe Markovchainfor smallt. We then investigatetwonotions of being close to a rapidly mixing Markov chain that fall within the framework of property testing, and show how to test that a given Markov chain isclose to a
THE STATUS OF THE P VERSUS NP PROBLEM relativizable proof can settle the P versus NP problem in either direction. Complexity theorists have used diagonalization techniques to show some NP-complete problems like Boolean formula ALGEBRAIC METHO DS FOR IN TERACTIV E PRO OF SYSTEMS IP of languages accepted b y in teractiv e pro of systems w as not m uc h larger than NP. In particular, it w as b eliev ed that co-NP-complete languages did not haFORTNOW FAMILY
The Fortnow Family. Lance Matt Molly Marcy Annie Matt Molly MarcyAnnie
LANCE FORTNOWPRESENTATIONSBIOGRAPHYRIBBITCOMPUTER OTHELLO PROGRAMSTUDENTSPUBLICATIONS Lance Fortnow. Dean of the College of Computing. Illinois Institute of Technology Email: lfortnow@iit.edu. Office: IIT Tower, 14th Floor, Room 14F9-1. Phone: (847) 579-9310. LANCE FORTNOW PUBLICATIONS Publications. Important Notes: The copyrights for journal and conference proceedings papers generally belong to the publisher of the journal or proceedings. All papers may be downloaded for personal or research purposes only. The PDF files are the most recent versions of each paper and may not correspond to the referenced version. THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE IMPOSSIBLE 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 aMORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
CHEC - LANCE FORTNOW Chec king Computations in P olylogarithmic Time L aszl o Bab ai 1 Univ. of Chicago 6 and E otv os Univ., Budap est L anc e F ortnow 2 Dept. Comp. Sci. Univ. of Chicago 6 onidPRESENTS RIBB IT
INSTRUCTIONS 1. Boot the Ribbit diskette and follow the directions in order to play. On the screen you will see: P-Play D-Demo Press the "P" key and you may play the game.AC - LANCE FORTNOW
Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e er ERRORS | THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE Errors. The errors below have been corrected in the paperback edition. In Figure 3-2 (page 34), David and Helen should not be friends. In chapter 2, I used the fictional name Milena Pavel for the Czech woman who settled the P versus NP problem. Pavel is the male form of the name – the female form is Pavlova. Whether Milena was married and ALGEBRAIC METHO DS FOR IN TERACTIV E PRO OF SYSTEMS IP of languages accepted b y in teractiv e pro of systems w as not m uc h larger than NP. In particular, it w as b eliev ed that co-NP-complete languages did not haFORTNOW FAMILY
The Fortnow Family. Lance Matt Molly Marcy Annie Matt Molly MarcyAnnie
LANCE FORTNOWPRESENTATIONSBIOGRAPHYRIBBITCOMPUTER OTHELLO PROGRAMSTUDENTSPUBLICATIONS Lance Fortnow. Dean of the College of Computing. Illinois Institute of Technology Email: lfortnow@iit.edu. Office: IIT Tower, 14th Floor, Room 14F9-1. Phone: (847) 579-9310. LANCE FORTNOW PUBLICATIONS Publications. Important Notes: The copyrights for journal and conference proceedings papers generally belong to the publisher of the journal or proceedings. All papers may be downloaded for personal or research purposes only. The PDF files are the most recent versions of each paper and may not correspond to the referenced version. THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE IMPOSSIBLE 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 aMORE P V NP
More P v NP. Lance Fortnow’s September 2009 Communications of the ACM article The Status of the P versus NP Problem that inspired this book. Gödel’s 1956 letter to von Neumann where he essentially describes the P versus NP problem fifteen years before Cook’s seminal paper. Computational Complexity (Lance Fortnow and BillGasarch)
CHEC - LANCE FORTNOW Chec king Computations in P olylogarithmic Time L aszl o Bab ai 1 Univ. of Chicago 6 and E otv os Univ., Budap est L anc e F ortnow 2 Dept. Comp. Sci. Univ. of Chicago 6 onidPRESENTS RIBB IT
INSTRUCTIONS 1. Boot the Ribbit diskette and follow the directions in order to play. On the screen you will see: P-Play D-Demo Press the "P" key and you may play the game.AC - LANCE FORTNOW
Ac kno wledgmen ts F oremost I w ould lik e to thank m y advisor, Mic hael Sipser. Mik e has collab orated on m uc h of m y researc h and virtually ev ery problem I ha v e er ERRORS | THE GOLDEN TICKET: P, NP AND THE SEARCH FOR THE Errors. The errors below have been corrected in the paperback edition. In Figure 3-2 (page 34), David and Helen should not be friends. In chapter 2, I used the fictional name Milena Pavel for the Czech woman who settled the P versus NP problem. Pavel is the male form of the name – the female form is Pavlova. Whether Milena was married and ALGEBRAIC METHO DS FOR IN TERACTIV E PRO OF SYSTEMS IP of languages accepted b y in teractiv e pro of systems w as not m uc h larger than NP. In particular, it w as b eliev ed that co-NP-complete languages did not haFORTNOW FAMILY
The Fortnow Family. Lance Matt Molly Marcy Annie Matt Molly MarcyAnnie
LANCE JEREMY FORTNOW ACADEMIC Major Invited Talks \The Early Days of Interactive Proofs," Computer Science Research Week, National University of Singapore, January 6, 2020. \Computer Science in Six-Tenths of a Second," Distinguished Lecture, University of KOLMOGOROV COMPLEXITY Kolmogorov Complexity Lance Fortnow 1. Introduction 010101010101010101010101 100111011101011100100110 110100110010110100101100 Consider the three strings shown above.PRESENTS RIBB IT
INSTRUCTIONS 1. Boot the Ribbit diskette and follow the directions in order to play. On the screen you will see: P-Play D-Demo Press the "P" key and you may play the game. LEARNING REDUCTIONS TO SPARSE SETS The least common notation we use, is: PNP k and FP NP, which are the classes of sets and functions, respectively, that are polynomial-time computable with non-adaptive queries to an NP oracle; PNP, and FPNP, the classes of sets and functions that are polynomial-timecomputable by
ARE COOK AND KARP EVER THE SAME? Theorem 5.1 There exists an oracle Band a sparse set A62PBsuch that for every set C C p B T A ()C B m A: Proof: Let M 1;M 2;::: be an enumeration of polynomial-time oracle Turing machines. Note thatC p B T Ais the same as saying there exist machines MTURING’S DOTS
Turing’s Dots Lance Fortnow Northwestern University Abstract Discussion of Turing’s paper \The Use of Dots as Brackets in Church’s Sys-tem," J. Symbolic Logic 7, pp 146-156 (1942) ROBUST SIMULATIONS AND SIGNI CANT SEPARATIONS Robust Simulations and Signi cant Separations Lance Fortnowy Georgia Institute of Technology Rahul Santhanamz Oxford University Abstract We de ne and study a new notion of \robust simulations" between complexity classes whichLANCE FORTNOW
Created Date: 5/13/2010 8:33:31 AM OPTIMAL - LANCE.FORTNOW.COM W e sa y a set A reduces to B if there exists p olynomial-time computable function f suc h that for all strings x, is in A if and only B. W e also call this an m-reduction, \m" forTHE FORTNOW FAMILY
LANCE MATT MOLLYMARCY ANNIE
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