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CSCI920 Grand Challenges in Computer Science Guilin Wang SCSSE August 2010

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Contact Info Room: Consultation times: - Mon.: 11-13pm - Wed.: 14-16pm URL: The slides of this lecture

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One Grand Challenge in Theoretical CS - P vs NP Challenges in Information Security More Grand Challenges Outline

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What is the P vs NP problem? Informally, this problem asks: For any problem, if a given solution can be efficiently verified can it also be efficiently solved by a computer? Quickly verify an answer Quickly find the answer? Grand Challenges in TCS: P vs NP

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Example: subset sum problem Does a subset of {-10, -4, -1, 3, 7, 8, 13} sum to 0? Yes. It is {-10, -4, -1, 7, 8} Generalized version: Given a set of n integers, is there any nonempty subset of this set adding up to 0? Easy to verify a proposed answer, but not easy to find a correct answer. So, subset sum is a NP problem. Source: Wiki Grand Challenges in TCS: P vs NP

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A more formal definition -P and NP are two complexity classes of problems -P: All problems that can be solved on a deterministic sequential machine in polynomial time, measured by the size of its input. -NP: All problems whose positive solutions can be verified in polynomial time, or equivalently, whose solution can be found in polynomial time on a non- deterministic machine. -So, is P = NP? Source: Wiki Grand Challenges in TCS: P vs NP

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Example Sudoku: Source: Wiki Grand Challenges in TCS: P vs NP

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Answer: Source: Wiki Grand Challenges in TCS: P vs NP

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o Does this mean Sudoku is a NP problem? Yes o Then, can we conclude that P=/= NP? No, two reasons: (1) In fact, we have not yet showed that there is no efficient algorithm to solve the problem, i.e. find a solution. (2) Even we can show point (1), it just means that Sudoku is a P problem, not necessary every NP problem in P! Grand Challenges in TCS: P vs NP

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NP-complete problems -Boolean function satisfiability problem (3SAT) -3 colouring problem -Bin-packing problem - Travelling salesperson problem Grand Challenges in TCS: P vs NP

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Source: Wiki

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Do mathematicians believe P=NP? According to a survey conducted in 2002, here are answers by 100 researchers: - No (61) - Yes (9) - Not sure (22) - Independent of the currently accepted axioms (8) Grand Challenges in TCS: P vs NP

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Why is P vs NP important? - A famous problem, proposed by Stephen Cook in 1971 (http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=805047).http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id= A 1m$ problem, promoted by the Clay Mathmatics Institute (http://www.claymath.org/millennium/)(http://www.claymath.org/millennium/ -More seriously, this is mental challenge for humans. Grand Challenges in TCS: P vs NP

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Why is P vs NP important? - Positively, a proof showing that P=NP could have enormous impact, if it can lead to efficient solutions for many NP problems. For examples, travelling salesman problem is important for logistics and operations research. - Negatively, if such a proof is constructive and efficient may lead to the collapse of modern cryptography, like public key encryption and Triple DES. Grand Challenges in TCS: P vs NP

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Why is P vs NP important? - This may cause revolutions in mathematics! ‘ If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss...’ Scott AaronsonScott Aaronson, MITMIT Grand Challenges in TCS: P vs NP

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Why is P vs NP important? - On the other hand, a proof showing that P=/=NP could also be a groundbreaking advance in complexity theory, and may guide new research directions as many research do not need to struggle to find efficiently solutions for enormous NP complete problems! Grand Challenges in TCS: P vs NP

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Claimed Proofs - Many people (amateur or professionals) have claimed proofs showing either P=NP or P=/=NP. -Here is a good website on this issue -A recent such claim is from Vinay Deolalikar, who is an IT researcher working Palo Alto, California. -Some fatal flaws in his proof were pointed out by Terrence Tao, who was awarded a Fields Medal in Grand Challenges in TCS: P vs NP

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However, nothing is impossible! In the last 20 years, we have seen two miracles in mathematics: -Fermat’s Last Theorem was proved by Andrew Wiles, Poincaré Conjecture was proved by Grigoriy Perelman in He didn’t accept the Fields Medal in 2006 and turned down Clay Mathematics Institute 1m$ award in Grand Challenges in TCS: P vs NP

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Grand Challenges in CS (Part II) Challenges in Information Security More Grand Challenges

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Challenges in Information Security (IS1): Shannon’s Theory of Secrecy Systems and Its Challenges in Modern Communications -Claude E. Shannon: Born in Michigan, on 30/04/1916, awarded PhD at MIT in The father of information theory. -He used mathematical methods to develop the theory of communications and cryptography. -E.g, entropy, random, pure, perfect and ideal types of cryptosytems. Grand Challenges in CS II

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Shannon’s Paradigm of a Secrecy System Grand Challenges in CS II

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-What is the essence of Shannon’s theory on secrecy systems? -What are the challenges for applying this theory to design secrecy systems for modern communications? Grand Challenges in CS II

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IS2: Challenges in the Formal Security Proofs for Public Key Cryptography. -Firstly, give formal definitions to specify attackers’ targets (=security requirements) and allowed actions (resources). -Then, construct a security scheme (i.e., algorithm or protocol). -Finally, prove such a scheme is secure under the assumption that a well known computational problem is intractable. Namely, if an attacker can compromise the system then he can solve the hard problem. Grand Challenges in CS II

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-Formal definitions (models) are complex, so they may be incomplete. -Subtle formal proofs are given by human beings, so they may contain flaws. -So, what are the challenges in this area? -And how can we do better? Grand Challenges in CS II

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IS3: Is cryptanalysis enough for designing secure symmetric cryptosystems? -Usually, the design of symmetric cryptosystems (hash functions, symmetric encryption algorithms etc) follows the paradigm design-attack-redesign. -Is it possible to guarantee that a newly released symmetric cryptosystem is immune to some or even all attacks? -What are the challenges in topic? Grand Challenges in CS II

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IS4: Challenges in design and implementation of secure systems -Security systems seemingly are much more complex than algorithms and protocols. -Do we have any systematic and efficient ways to design and implement secure systems? -Naturally, we also require usability. -Where do the possible challenges come from? Grand Challenges in CS II

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Other Grand Challenges in Computing -The topics in this part are adapted from the following report: Grand Challenges in Computing Research 2008, edited by J. Kavanagh and W. Hall. BCS and IET, URL: (and click `GCCR'08 Final Report’)http://www.ukcrc.org.uk/grand-challenge/index.cfm Also, Grand Challenges in CS II

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GC1: Modelling Living Processes - Biology is fundamentally about regulatory systems, though there are a lot of stuff like viruses, genes, enzymes, energetics. - In biology, computing is key to design, modelling and implementation. - In the human genome project, the gene sequence analysis was mainly about algorithms and computing. - Challenges in this topic are to design super-models, which are expected to be dynamic, to grow and interact with environments. Grand Challenges in CS II

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GC2: Ubiquitous Computing - During the last decades, the our society has been evolved from the mainframe era (many people share one computer) through the PC era to the mobility era, and will move to ubiquity era (one person relates to thousand or more computing devices). - Ubiquitous devices are in place for use, but there are challenges in the science of ubiquity: *Interconnecting theory, systems and human interaction *Societal, legal and political consequences * … Grand Challenges in CS II

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GC3: Memories for Life -Our memories have significance influences on almost every aspect of our life and work. -In the coming 20 years, it will be possible to put an entire waking life on a laptop disc. -This raises many challenges in different CS areas: AI: Indexing, clustering, automatic annotation, … Image Processing: Visualisation & Virtual Reality: Security & Privacy: …… Grand Challenges in CS II

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Here are more challenges in multimedia: (http://comminfo.rutgers.edu/conferences/mmchallenge/(http://comminfo.rutgers.edu/conferences/mmchallenge/) -3DLife Challenge 2010: Sports Activity Analysis in Camera Networks -Google Challenge 2010: Robust, As-Accurate-As-Human Genre Classification for Video -Google Challenge 2010: Indexing and Fast Interactive Searching in Personal Diaries -HP Challenge 2010: High Impact Visual Communication -Radvision Challenge 2010: Video Conferencing To Surpass “In- Person” Meeting Experience -Radvision Challenge 2010: Real-time Data Collaboration Adaptation for Multi-Device Video Conferencing Grand Challenges in CS II

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GC5: The Architecture of Brain and Mind -The entire grand challenge is to design and build a humanoid robot, which is capable to do a range of sophisticated behaviour, in some sense equivalent to the intelligence of a 2-4 years old child. -Difficulties mainly come from neurological reality to abstract computer models. Grand Challenges in CS II

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GC7: Journeys in Non-classical Computation -Motivation: Could we do new kinds of computations, if our computers were built from different stuff or organized in different ways? -Classic computing paradigms: Turing: Know resource requirement before doing computation Von Neumann: stick to sequential fetch-execute-store codes - Can we apply bio-inspired algorithms into areas like neural problems and social networks? Grand Challenges in CS II

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GC8: Learning for Life -Regarding to learning technologies, we are still in the Stone Age. Can we drive computing technologies into a stage that enables every learner can efficiently learn whatever they want to learn, at any level, in any way, without restrictions on their ages, their locations and their literacy levels? -The challenges include how to conceptualise learning environments and understand learning processes, as well as what learning for life will be like. Grand Challenges in CS II

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