Informação e Computação para a Inteligência Artificial

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1 Informação e Computação para a Inteligência Artificial Andreas Wichert MEIC Tagus (Página da cadeira: Fenix) Objectivo Geral Apresentaremos uma visão compreensiva da ciência da informação como uma parte fundamental das áreas da inteligência artificial e da computação Exemplos na teoria da computação, que levarão às ideias de Qubits e à possível maneira de simular um computador quantum, serão fornecidos A simulação de software com a utilização do Mathematica será realizada para o suporte à explicação das ideias por trás dos computadores quantum 1

2 Organization Program Introduction Corpo docente Andreas Wichert - Teóricas / Práticas andreas.wichert@tagus.ist.utl.pt andreas.wichert@inesc-id.pt 2

3 Organização das aulas Teóricas: Matéria (slides baseados no livro e artigos e...) Práticas/Laboratório (weekly!): Exercícios Software Experiments Avaliação Problemas praticas (Exercícios) (40%) + Exame orais (60%)! 3

4 Bibliografia (Main) Howard L. Resnikoff. The Illusion of Reality. Springer-Verlag, 1987 Colin P. Williams and Scott H. Clearwater. Explorations in Quantum Computing, Springer- Verlag 1997 Bibliografia Quantum Computing, Mika Hirvensalo, Springer-Verlag, 2001 Complexity, Entropy and The Physics of Information, Wojciech H. Zurek, Addison- Wesley,

5 Programa 1. Introduction 2. Entropy - Information 3. Information 4. Information Measurement 5. Physical Information measurement 6. Principles of Information-Processing Systems and Signal Detection Programa 7. Biological Signal Detection and Information Processing 8. Hierarchical Neural Networks 9. Associative Memory and Information Theory 10. The capabilities of computing machinery 11. Quantum Mechanics and Computers 12. Quantum Computers 5

6 Programa 13. Effects of Imperfection 14. Breaking Unbreakable Codes 15. True Randomness 16. Quantum Cryptography 17 Crover`s Search Algorithm 1 18 Crover`s Search Algorithm 2 Programa 19 Quantum Teleportation 20. Quantum Error Correction 21. How to make a Quantum Computer 22. Complexity Lower Bounds for Quantum Circuits 23.AI, Entropy and The Physics of Information 24. The New AI and its applications 6

7 What is Information? Information first began to assume an independent and quantifiable identity in the research of physics and psychologists in the second half of the nineteenth century... It grew in importance with the development of electrical-based communication systems Emerged as a unifying and coherent scientific concept along with the invention and development of computers The subject matter of a science of information is abstract, for it concerns not the substance and the forces of the physical world (?) 7

Representation Symbolic tokens are necessarily

represented by the electrical and biochemical states

physical sciences with the proper subject matter of

.. Information can be presented in a variety of

8 Representation Symbolic tokens are necessarily represented by physical phenomena thoughts are represented by the electrical and biochemical states of the neural network There is an intermixing of the physical sciences with the proper subject matter of information science... Information can be presented in a variety of forms which differ inessential from one another Natural language Symbols Acoustic speech Pictures 8

9 Information is what remains after one abstracts from the material aspect of the physical reality... How to do it? Scientific study of information cannot be separated from systems which are capable of bearing information Information database and a user Meaning - Information Information has an independent reality, meaning does not Meaning involves the interpretation of the information in relation to some context Information exists It does not need to be perceived to exist 9

composed of an indefinite and perhaps infinite number of hexagonal

10 Information = Pattern What is a pattern? Find measure of it... The Library of Babel The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings Jorge Luis Borges ( ) 10

11 The books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks) Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books The library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages 11

12 Despite - indeed, because of -this glut of information, all books are totally useless to the reader Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God The Library contains books Just one "authentic" volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe 12

13 Constraints In a language Some letters are more frequent then others Some combination of letters are less probable History - Physics and Information Thermodynamics is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics 13

14 Suggestions thermodynamically descriptions are not descriptions of physical properties and relationship themselves, but of some other still more fundamental property coeval with all regimes of physical inquiry Thermodynamically relations might remain valid for all physical theories which can describe an aspect of nature Thermodynamically quantities link physical entities to their organization, to their informational properties, and that the informational structure Probability enter into thermodynamically considerations and opened as road for abstractions and generalization 14

15 Selective Omission of Information Sensory data is corrupted and modified by sensing organism in ways which greatly reduce its quantity and substantially modify its original form Retaining essential information What is an A? What makes something similar to something else (specifically what makes, for example, an uppercase letter 'A' recognisable as such) Metamagical Themas, Douglas Hoffstader, Basic Books,

surpasses the ability of any computing machine to explore it completely The

16 Chess Game tree in chess playing, which determines all possible consequences of alternative plays has a combinatorial complexity which surpasses the ability of any computing machine to explore it completely The complexity is however reduced by selectively omitting most of the pathways (heuristics) 16

17 The omitted ones are expected to be unproductive Selective omission in context of a decision problem which involves searching through a complex tree the application of heuristics procedures AI-Example: Blocks World planing with and without similarity heuristic similarity to the target state represented as picture 17

18 Measurement Eye us sensitive to photons of light which are governed by the wave-particle duality of quantum physics Breakdown of classical physics, was due to the improper extension of naïve concepts of measurement from the realm of everyday life Accuracy of measurement of the position of an object interfered with the accuracy of measurement of its velocity of motion (momentum) All physical measurements are, ultimately statistical in the sense that repeated measurements of identical physical situations will not lead to identical results, but only measurements which are collectively related to one another by a statistical law 18

19 Measurement, some information is lost, and whenever a measurement is performed, and that the degree of organization of the universe continually decreases Digital - Analog 19

Computation The information which went into the computer is different from what came out The most influential model of computation is the Turing Machine The Idea of the Turing Machine grew out of on

20 Computation The information which went into the computer is different from what came out The most influential model of computation is the Turing Machine The Idea of the Turing Machine grew out of on attempt to answer a question proposed by the German mathematician Hilbert in the 1900 in the International Congress of Mathematics held in Paris concerning that he be lived to be the 23 most challenging mathematical problems of the day 20

21 The possibility that quantum mechanical effects might offer some thing genuinely new was first hinted by Richard Feynman of Caltech 1982 when he showed that no classical TM could cimulate certain quantum phenomena without incurring an exponential slowdown, but that a unversal quantum simulator could do so Quantum TM has the potential for encoding many inputs to a problem simultaneously on the same tape and performing a calculation on all inputs in the time it took to do just one of the calculations classically... 21

22 Quantum computers could compute certain outputs, such as true random numbers, that are not computable by any deterministic TM There is no function that generates true random numbers Quantum parallelsism All the outputs are computed in the time taken to evaluate just one output classically Unfortunately, you cannot obtain all of these outputs explicity because a measurment in the final supeposed state would only yield one output! In principle a QTM could be used to create a proof that relied upon quantum mechanical inference among all the computations going on in superposition Upon interrogating the QTM for an answer you might be told yes your assumption is true but there would be no way to exibit all computation steps that had gone in order to arrive at the conclusion... 22

23 Worse, if you tried to peek inside the QTM as it is working, to get some information about the state of the proof at that time, you would invariably disrupt the future course of the proof... Organization Program Introduction 23

Informação e Computação para a Inteligência Artificial!

Informação e Computação para a Inteligência Artificial! Andreas Wichert!! MEIC Tagus! (Página da cadeira: Fenix)!! Objectivo Geral! n Apresentaremos uma visão compreensiva da ciência da informação como