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AWARD DECISION INFORMATION AND COMMUNICATION TECHNOLOGIES Madrid, January 11, 2016. The jury in the eighth edition of the BBVA Foundation Frontiers of Knowledge Awards in the Information and Communication category, formed by: CHAIR OF THE JURY Prof. Georg GOTTLOB Professor Computer Science Department University of Oxford United Kingdom MEMBERS Prof. Oussama KHATIB Professor of Computer Science and Director of the Robotics Laboratory Stanford University USA Prof. Dr. Rudolf KRUSE Professor Faculty of Computer Science Otto-von-Guericke University Magdeburg Germany Prof. Mateo VALERO Director Barcelona Supercomputing Center Spain Prof. Joos VANDEWALLE Head of SCD Division Department of Electrical Engineering Katholieke Universiteit Leuven Belgium SECRETARY Prof. Ramón LÓPEZ DE MÁNTARAS Director Artificial Intelligence Research Institute Spanish National Research Council Spain Meeting together on January 11, 2016 in the offices of the BBVA Foundation in Madrid, Spain, in order to deliberate and decide, have resolved to grant the BBVA Foundation Frontiers of Knowledge Award in the Information and Communication Technologies category, in its eighth edition, to the following candidate: Professor Stephen Arthur COOK, Department of Computer Science, University of Toronto Nominated by: Professor Sven Dickinson, Chair of Computer Science Department, University of Toronto, Canada Citation: The BBVA Foundation Frontiers of Knowledge Award in the Information and Communication Technologies category has been granted in this eighth edition to Professor Stephen Arthur Cook from the University of Toronto, Canada, for his pioneering and most influential work on computational complexity. Cook´s work plays an important role in identifying what computers can and cannot solve efficiently. His concept of “NP-completeness” is considered as one of the fundamental principles in computer science and has been making a dramatic impact on all fields where complex computations are crucial. In his seminal 1971 paper “The complexity of theorem proving procedures” Cook gave a mathematical meaning to “efficiently computable”: A problem is efficiently computable if it is in the class P of problems computable in deterministic polynomial time. He also gave a mathematical meaning to “efficiently verifiable”, as in polynomial time, once a solution is given. An efficiently verifiable problem, if at all solvable, can be solved with a guess-and check procedure by first guessing a candidate for a solution (the so-called nondeterministic guessing step), and then verifying efficiently that the guess is indeed a solution (the deterministic polynomial-time checking step). Therefore the class of these problems is referred to as NP for nondeterministic polynomial-time. An example of a problem in the class NP is the well-known traveling salesperson problem: given a number of cities and distances between each pairs of cities, is it possible to visit all cities by a tour whose total travelled distance is smaller than a given bound? Once an appropriate tour has been guessed, it is easy to verify in polynomial time that the total travel distance is below the desired bound. Therefore this problem is in NP. However, with a growing number of cities this problem becomes very hard to solve, and no efficient (polynomial time) algorithm for its solution is known. For many other highly relevant computational problems in the class NP, no efficient algorithm is known. However, it has so far been impossible to prove that these problems cannot be solved efficiently and actually require exponential time for their solution. Cook established the now well-known P versus NP question as to whether or not every decision problem that is efficiently verifiable (in NP) can be made to be efficiently computable (in P) and conjectured (now known as Cook’s Hypothesis) that P≠NP. The P versus NP question is now one of the seven million “Millennium Prize Problems” listed by the Clay Mathematics Institute. Cook showed that there are specific problems within the class NP to which all other problems in NP can be efficiently transformed. These problems are referred to as NP-complete problems. If one NP-complete problem can be solved in polynomial time, then all can. 45 years of combined efforts by Computer Scientists and Mathematicians have not found any polynomial-time algorithm for any NP-complete problem. Today there are literally thousands of known NP complete problems in fields as diverse as biology (e.g. protein folding), physics, economics, number theory, logic, optimization, and any field which has computational issues. NPcompleteness not only provides important guidelines to scientists but also to software engineers and practitioners. Every undergraduate Computer Science curriculum typically includes lectures about NP-completeness. Although Cook’s seminal paper on NP-completeness is his best known contribution to theoretical computer science, he has made equally deep and important contributions in the area of proof complexity, in particular with regard to the complexity of propositional proof systems and theories of bounded arithmetic. Cook’s influence goes well beyond his own research. He is a spectacular teacher, an excellent advisor, and an overall leader within the mathematical and computer science communities. And in witness whereof sign the present document in the place and on the date first above written. CHAIR OF THE JURY Prof. Georg Gottlob MEMBERS Prof. Oussama Kathib Prof. Dr. Rudolf Kruse Prof. Mateo Valero Prof. Joos Vandewalle SECRETARY Prof. Ramón López de Mántaras