Artificial Intelligence     Kismet, a face bot. The parts of his     face move to show emotion.        An Isearch research...
Introduction     For years now, humans have been working with Artificial Intelligence, tryingto create intelligent machine...
intelligent computer programs. It is related to the similar task of using computersto understand human intelligence, but A...
end of the imitation game, A would try to guess which of B and C is the computer.If A does not know or gets it wrong, then...
invented two giant machines. His first, the difference engine, could do advancedmathematical problems. He made a working m...
for the opponent. This will consume a long time for the program to respond toeach move. It would also need a large amount ...
they were to use Brute Force, the program would have taken all the space andtime in the universe. So Newell and Simon’s st...
1- Most Computers do not learn from experience. If a computer was learning towalk, it wouldn’t try to put different muscle...
today in a class of computer programs called “expert systems”. These systems useinformation from human experts such as doc...
that in the future, surgeons in one country will be able to do surgery on a patientin another country.    Robots come in a...
bonds with her, and some psychiatrists asked Weizenbaum if they couldrecommend human patients to her. Eliza does this so s...
GamesVelenaWhat is Velena?     Velena is a Connect-4 computer game that uses AI. It is based on a thesis byL. Victor Allis...
TerminologyOdd Square: A square that is in an odd rowEven Square: A square that is in an even rowA Group: Four men connect...
instead, the program tries to predict the outcome of the game using mathematics.     When constructing a Connect-4 program...
Fig 3.                  Illegal?     The answer is yes. Since white starts the only possible position that theycould have ...
When using Velena, you will notice that you cannot change the board sizefrom a standard 7x6 board. This is because of a pr...
said.        Although Deep Blue was smart, it did no think in the same way that humansdo. That is still many years and bre...
of three days. In the end, Malcolm Davis won only by eight points. The neural netof the backgammon-playing program has 300...
turn, they must remove the same number of marbles from each of two differentjars. If a player is unable to do so, they los...
2/3/5(W)   0/1/5(W)                                      0/3/3(W)                                      1/2/5(L)   0/1/5(W)...
b)(Hypatia ’03) Xavier and Yolanda are playing a game starting with some coins  arranged in piles. Xavier always goes firs...
•Binary Logic: Also called Boolean Logic. The point of Boolean Logic is to represent a function of a logic gate (Logic gat...
humanity’s current strengths over AI.•Household Chores: AI operated robots will be able to wash dishes, control air condit...
our research position and knowledge of AI is about the same as the state ofPersonal Computers in 1978. Ray Kurzweil, the a...
!    Canada: Crabtree, 1999Hyland, Tony. How Robots Work. Minnesota: Smart Apple Media, 2007Flanagan, David. Java in a Nut...
McCarthy, John. http://www-formal.stanford.edu/jmc/whatisai/node1.html. Stanford,!   2007Rudnik, John. http://www.math.ca/...
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  1. 1. Artificial Intelligence Kismet, a face bot. The parts of his face move to show emotion. An Isearch research paper By: Andrew Ilyas May 13, 2010
  2. 2. Introduction For years now, humans have been working with Artificial Intelligence, tryingto create intelligent machines. Machines that are faster and smarter than thehuman brain. One question that still remains unanswered in AI is whether acomputer will ever be smarter than mankind. This research discusses the use ofAI in fun games, and attempts to answer the question stated above. It explainsand gives different definitions for Artificial Intelligence, covers the history andsearch methods. Also, it will highlight on some of the applications of AI beingused in Robotics. In addition, the paper introduces Game Theory and talks aboutthe future of Artificial Intelligence. Finally, it concludes by answering my BigThink question stated above, and provides further references in AI for interestedreaders.What is AI?Definitions of AI “AI is the science of making machines do things that would requireintelligence if done by men”- Marvin Minsky, MIT “The field of computer science that seeks to understand and implementcomputer-based technology that can simulate characteristics of humanintelligence”-The Facts on File Dictionary of Artificial Intelligence, by RaoulSmith “Computers with human-level intelligence; computer programs that performtasks once thought to require human flexibility and judgment”- ArtificialIntelligence, by Philip Margulies “It is the science and engineering of making intelligent machines, especially
  3. 3. intelligent computer programs. It is related to the similar task of using computersto understand human intelligence, but AI does not have to confine itself tomethods that are biologically observable.” John McCarthy “The capability of a device to perform functions that are normally associatedwith human intelligence, such as reasoning and optimization throughexperience.”-[1]The Turing Test Alan Turing (1912-1954) was a British Mathematician famous for the Turingmachine. The Turing machine was a theoretical computer that includes a headthat can read and write, and an infinite tape. The head will read, and dependingon the input, will either move left or right. He is also famous for cracking theGerman Code Enigma. Right now, Turing is so respected that the highest honoryou can get in computer science is the Turing award. One of the common questions discussed when working with ArtificialIntelligence is “How do we know when machines are intelligent?” Does it have toexcel in every topic, or be good at one? Do machines have to be aware of theirown existence? Some argue that if a machine is equal to a human in all fields, thatthe machine is intelligent. When Mind Magazine asked Alan Turing “CanMachines Think?” He took all these definitions into consideration, and then cameup with a test. Turing called his test “imitation game”. It would consist of threeintelligent beings, two humans and one computer. Just so it does not get tooconfusing, let the two humans be A and B, and the computer be C. A would have along typed conversation covering many topics with B and C. It must be typed andin separate rooms, because the way C speaks or how it looks like should not affecthow intelligent it is. If A, B, and C are all in the same room during theconversation, A would know that C was a computer. Also, A must cover manytopics, so that C cannot impress A with its great knowledge in one topic. At the
  4. 4. end of the imitation game, A would try to guess which of B and C is the computer.If A does not know or gets it wrong, then the computer is intelligent. This “Turingtest” is often mentioned when the progress of AI is discussed.History For a machine to be intelligent, it must be able to reason, learn fromexperience, set goals for itself, and adapt to the world around it. A machine thatcan do these things is the machine that humans have been trying to build for along time. In 1642, Blaise Pascal invented the first “computer”. In our days this wouldbe called a calculator, but back then, anything that could do advancedmathematical calculations was called a computer. Since his father was a taxcollector, Pascal invented his machine to help his father count the taxes. Thiscalculator could add and subtract. This invention was also the birth of artificialintelligence. Inspired by Pascal, the philosopher and mathematician Gottfried Leibnizmade a more sophisticated machine that could add, subtract, multiply, and findthe square root of numbers using gears and pulleys. These mathematicians ledthe way into computers and artificial intelligence. For example, Gottfried Leibnizdid not like the English language for computing that was being used then. In his“new” language, no two words meant the same thing, and no word meant twodifferent things. Although the technology of the 1600’s was not advanced enoughfor his language, Leibniz’s “perfect language” is the foundation for theprogramming languages that we use today. The 1840’s mathematician Charles Babbage almost made the first computerin the modern sense. In the 19th century, the government needed a great deal ofcalculations to be done. Thousands of people did this job, but it was boring,needed lots of concentration, and had many errors. To take this job over, Babbage
  5. 5. invented two giant machines. His first, the difference engine, could do advancedmathematical problems. He made a working model of this, but did not haveenough money to finish the machine. His second, more ambitious machine wasthe analytical engine. This was an ongoing project, but could not be finishedbecause of the primitive technology of the 1800’s. In the next hundred years, the world needed computers. Finally, the firstcomputer was built in 1951. The inventor is still debated on. As the years advance,computers get faster, and their parts get twice as small and compact, but it isalways the same design as the computer in 1951. (See AI Over Time section fortimeline, explanation, further AI history, and my future AI timeline)Game Search MethodsBrute Force Although some AI programs can do intelligent tasks faster than humans can,they do not think in the same way. Computers are much faster, have a biggermemory, and can search larger databases than humans. What Brute Force (alsoknown as exhaustive search) does is make use of all the advantages of thecomputers over humans. It makes use of the fact that every transistor in acomputer is about one million times faster than the human brain. It searches allpossible ways that a program can do something, and then picks the best one. The advantage to Brute Force is that it is always right. This is because it isexamining all the possibilities, so it cannot miss the best solution. Since computerparts have been getting smaller and more powerful, programmers have had morefreedom to use Brute Force. The main disadvantages to Brute Force are that it takes a long time, needslarge memory, and sometimes takes up a lot of space. For example, if Brute Forceis being used for something like playing a game of chess, this might be a problem.The program would need to search all possible moves for itself (as a player) and
  6. 6. for the opponent. This will consume a long time for the program to respond toeach move. It would also need a large amount of space to store the information.In fact, some problems are categorized because the only correct solution you canfind for the problem is by using the Brute Force method. These are called NP-Complete problems, which means that their most efficient complexity is (aconstant) to the power of n, where n is not a constant number. An example of an NP-Complete problem is the Knapsack Problem. You havea knapsack that can only carry a certain weight. You have n items. Each item hasa value and a weight. The Knapsack Problem asks for the placement of objectsinside the knapsack such that it will have the greatest value, but not surpass theweight that the knapsack can sustain. In this case, the most efficient algorithmhas a complexity of 2n x θ. Theta is a symbol used to represent a constant numberin complexity theory. Although Brute Force is always right, it still does not think like the humanbrain does. After all, many scientists point out, airplanes are not expected to flylike birds. When the future of AI is debated, the comparison between humanintelligence and machine intelligence is usually brought up. Brute Force is one of the many search algorithms used in AI. Others thatwere not listed are MinMax, Alpha-Beta pruning, A* search, Blind search, etc.Heuristics Heuristics are rules that are set to narrow down computers’ searches. Thissaves the computer from having to use Brute Force and look at all possibilities.This guessing problem was one of computers’ limitations before heuristics. Theprogram Logic Theorist (LT), made by Allen Newell and Herbert Simon, two AIpioneers, first addressed it. Logic Theorist was made in the 1950’s and designed to prove already knownmathematical theorems. Since the search space for theorem proving is infinite,they could not use Brute Force like programmers did with everything until LT. If
  7. 7. they were to use Brute Force, the program would have taken all the space andtime in the universe. So Newell and Simon’s strategy was to teach the computerto make educated guesses, almost like the way that humans make decisions. Ifhumans made decisions the same way that computer programs did before LT,they would be overwhelmed all the time. Simon and Newell called all their“guessing rules” heuristics. Nowadays, heuristics allow programs to make fast responses and narrowsdown their search to what usually works, not everything. FingerprintIdentification systems and Credit Card Fraud Identification both use heuristics tonarrow down searches. Other systems that use heuristics are the expert systemsthat predict the weather treat diseases, and book airplane flights.Applications of AILimitations and Advantages of Computers Before discussing the applications of AI and the use of computers in theseapplications, this section summarizes the advantages and limitations of usingcomputers.Advantages:1- Can calculate problems that would take humans years, and can do them inseconds. For example, in the Deep Blue vs. Kasparov Match, Deep Blue couldcalculate 200 million chess positions a second, while man can only do 2 a second.2- Giant Long- Term Memory. For example, in the Deep Blue vs. KasparovMatch, Deep Blue remembered every single move that Kasparov had made.3- Does not fatigue. For example, Fingerprint identification and Credit CardFraud check are two things which have been enhanced with AI because of theability to not get tired of what they are doing.Limitations:
  8. 8. 1- Most Computers do not learn from experience. If a computer was learning towalk, it wouldn’t try to put different muscles together like a baby would, but itwould follow a specific set of instructions to walk.2- Cannot make quick decisions based on experience3- Cannot make connections. For example, if a Google searcher searched “GeorgeWashington”, it might get him info about George Washington Baked Beans,Washington Ave., and the first president, although if you are looking up GeorgeWashington, you are probably searching for information about the firstpresident. This may annoy some searchers.4- Cannot understand the human language. If I said, “I hate pepper”, this couldmean many things. It could be a response to “I hate horses”, or someone might beoffering you pepper, or someone might say, Joe Pepper is coming to the movieswith us, and in response you might say, “I hate pepper”, but a computer wouldnever understand the difference.Neural Networks A Neural Network is a program designed to simulate the human brain andits neurons. People have found similarities between computers and the humanbrain long ago. But since then, some big differences have been found. Forexample, computers do not learn by trial and error, but instead they follow aspecific set of instructions that tell them what to do. Neural networks try to learn in the same way that a baby would learn towalk. Instead of following a set of instructions, the baby moves one muscle at atime. Sometimes the baby succeeds, and sometimes it fails. Each move that ittakes is directed by the brain and accompanied by a connection of the neurons inthe brain. If the baby fails to walk, the connection of neurons that produced thefailing movement would be shut down. If the baby succeeded, the neuralconnection will be kept open. Computer learning skills that are developed for neural networks are used
  9. 9. today in a class of computer programs called “expert systems”. These systems useinformation from human experts such as doctors, lawyers, etc. to make the kindsof decisions that the experts would make themselves. Expert systems also learnfrom experience and get better at their job the longer they are doing it. Fingerprint Identification is one of the many jobs made easier by expertsystems. The police needs to compare fingerprints found at a crime to thousandsof other fingerprints across the country. The reason why expert systems helpfingerprint identification is that the job needs the ability to recognize patterns, ahigh degree of judgment, and the inhuman ability to not get tired of working.Another problem that is made easier by expert systems is the detection of creditcard fraud. This also requires a high degree of judgment and the ability to searchthrough loads of data. What the credit card fraud identification expert systemdoes is that it uses artificial intelligence and scans all transactions made on thecard. It then reports any suspicions of credit card fraud to a manager. NeuralNetworks can do a lot for the modern world.Robotics 200 years ago, people who did mathematical problems were calledcomputers. Today, computers are complex machines that contain electricalcircuits that store loads of information in code. Also, the computer is used tocontrol the most complex machine ever invented by man - the robot. Robots canwork in any condition, without getting tired, and can do it faster than humans. The word “Robot” was first used by Karel Capek in his play “RUR (Rossum’sUniversal Robots)”, a play about robots that took over their masters. Anyway, theword “robot” originated from the Czech word “robota,” meaning, labour. When itwas first used, it had no exact definition. Virtual Reality is a new invention that uses our modern technology in adifferent way. By linking our sight, hearing and touch to the computer withsensors, Virtual Reality may be a giant breakthrough for AI. Scientists believe
  10. 10. that in the future, surgeons in one country will be able to do surgery on a patientin another country. Robots come in all shapes and sizes, but the most common is the mechanicalarm. This is also one of the simplest robots around us today. Scientists describethe ways that robots can move as their Degrees of Freedom. Robots with onehinge joint have one degree of freedom, while industrial robots that can move atthe waist, arms, elbows, etc., can have six degrees of freedom. Another type ofrobot is a face bot. A face bot is a robot that is shaped like a human face and canshow emotions on it. Kismet, a face bot, does not look completely human, but hecan move his ears, eyes, eyebrows, eyelids, and mouth to show differentemotions. Robotic AI can be used in many ways. For example, college students realizedthat they could program Lego robots to play soccer and started an internationalsoccer tournament called Robocup that featured a ball that sends out infraredsignals. Now, the Robocup has a junior section for elementary school, middleschool, and high school students. Each year, they meet to see who has the bestrobot. The activities at Robocup Jr. include an Aibo (Programmable robotic dog)Soccer League, dancing, and a robot rescue game, which simulates a real roboticrescue. Another use of Robot AI is in factory work. In factories, Robots weldsmash, put together, and load materials. This needs the ability not to fatigue andto be able to work in any condition. Another type of robot is a chatterbot. Chatterbots are online robots thatinteract with humans and can encage in a conversation. Chatterbots are not ascomplex as they seem, but they hide all their faults by redirecting theconversation to you. For example, in 1996, Joseph Weizenbaum made Eliza. Elizawas a relatively simple program that turned around people’s phrases. Forexample, if you said “How are you doing?” instead of saying "Good," or "Bad," itwood redirect the sentence and say " Why are you so interested whether I amdoing or not?" When Eliza first came out, many people made strong emotional
  11. 11. bonds with her, and some psychiatrists asked Weizenbaum if they couldrecommend human patients to her. Eliza does this so she does not have to answerthe questions that might trip her up. By asking you personal questions, she makesthe “patient" think about him instead of thinking about her mistakes. Also, theonline chat rooms and instant messaging make it easier for people to acceptEliza. Honda Japan leads the worlds humanoid robots with Asimo, the mostadvanced humanoid robot in the world. A humanoid robot is a robot that tries tosimulate humans. He has two legs, two arms, and a head. These kinds of robotsare the hardest to program, because, unlike humans, they do not have naturalbalancing systems. Asimo is 51 tall and 18 wide and weighs 115 pounds. He isconstructed with magnesium alloy and coated in plastic, which allows him to bevery lightweight and durable. Asimo has three indicator lights:1. White- Ready for operation2. Red- Ready to walk3. Green- Low-level power on A 51.8V Lithium-ion battery that lasts for an hour after a single chargepowers him. The battery takes up about thirteen pounds of Asimos weight and isstored in his backpack. He was built with 34 degrees of freedom and opposablethumbs. Also, with visual sensors on his head, and kinesthetic (force) sensors onhis wrists, Asimo can synchronize with human movement. Asimos running is atabout 6km/h and his stride is about 1.7 long. Asimos intelligence abilities are:1. Charting a course- The ability to chart a course around obstacles2.Recognizing moving objects3.Distinguishing sounds4.Recognizing faces and gestures One of the limits to robots is that they cannot do anything or respond toanything outside their program.
  12. 12. GamesVelenaWhat is Velena? Velena is a Connect-4 computer game that uses AI. It is based on a thesis byL. Victor Allis. Velena uses a known mathematical approach that consists of eightrules. With these rules, Velena can win the game if she plays first, no matter howwell her opponent plays. The program is a Shannon C-Type Program. Thismeans it uses a knowledge-based approach and tries to simulate the human mindto take decisions.Rules and Terms of Connect-4 Each game can be described as a sequence of moves, which means that if welabel every column with the letters a through g, and the rows 1 through 6, we candescribe every move, and therefore, every game, as a sequence of moves. Forexample, the game in Fig. 1 can be described as:Moves O X1 d1 e12 e2 f13 f2 g14 g2 d25 f3 c16 e3 d37 f4 f58 g3 e49 g4 ++where ++ symbolizes the end of the game, (the inability to move).
  13. 13. TerminologyOdd Square: A square that is in an odd rowEven Square: A square that is in an even rowA Group: Four men connected, vertically, horizontally, or diagonallyA Threat: Three men of the same type (X or O) connected, and with the fourthsquare that forms the group empty and the square below it emptyOdd Threat: A threat where the empty square that completes the group is an oddsquareEven Threat: A threat where the empty square is evenDouble Threat: There are two groups which share an empty odd square;Each group is filled with only two men (of the same color) and the other twosquares (one for each group) are empty and are one above the other. The squarebelow the shared square must be empty too.Game Strategy Before we start to construct a game strategy, let it be noted that we areconsidering white as O and black as X. The first step in constructing a gamestrategy is noting that after white has moved, the number of squares left on theboard are odd, and that after black has moved, an even number of squares areleft. From this it was proven that if white has an odd threat, and black cannotconnect 4 men anywhere, white will eventually win, and the same with black if ithas an even threat and white cannot connect four men anywhere. If white has anodd threat and black has an even threat, and the two threats are in differentcolumns, white will win. If they are in the same column, the lower threat will win. Velena’s strategy differs depending on if she plays white or black. When sheis white, she uses her database to always get to an odd threat position, and thenwin the game from there. When she is black, she follows the longest winningroute for white and tries to stop it. To use brute force with Velena, it would take up terabytes of space, so
  14. 14. instead, the program tries to predict the outcome of the game using mathematics. When constructing a Connect-4 program, there are two strategies used. Thefirst one tries to stop your opponent from winning, but trying to connect 4 men atthe same time. This strategy guarantees invulnerability in the short run, buttends to fail on the long run, because it cannot see past the first few moves of thegame. The second strategy is to take a win on the long run. Most Connect-4algorithms implement the first strategy with a variation of Alpha-Beta Pruning, atype of search method.Game Complexity In a Connect-4 board, each slot has three states: either it’s occupied bywhite, occupied by black, or not occupied at all. Since there are 42 slots (7columns x 6 rows), our game complexity would be 3(possible states of a1) x 3(possible states of a2)... etc., which would be 342. This is approximately 1020. Butthis is an upper bound complexity, since we are counting all the illegal positionsas well. After subtracting the number of illegal positions, we get 71 x 1012, which isstill a very large number. Although Connect-4 is not as trivial as Tic-Tac-Toe, itsgame complexity is not as large as that of chess, and most of the moves arerepeated. For example, for white to win, the first seven moves are forced, so theyrepeat a lot. One problem there is with calculating the game complexity of Connect-4 ischecking if a position is illegal. This can be very hard sometimes. For example, isFig 3 illegal?
  15. 15. Fig 3. Illegal? The answer is yes. Since white starts the only possible position that theycould have played is d1. If black played b1,d2, or f1, white would not have a move.So black can play a1, c1, e1, or g1. Let’s say black played a1. The only move whitehas is a2. Similarly, the only moves black has that can be responded by white arec1, e1, and g1. If this cycle goes on the farthest we will ever get is Fig. 4: Fig. 4 Closest we can get to Fig. 3Fig. 3 and Fig. 4 demonstrate the difficulty to detect positions’ legality. Thisfactors in to building a Connect-4 program’s database and figuring out the gamecomplexity.Board sizes
  16. 16. When using Velena, you will notice that you cannot change the board sizefrom a standard 7x6 board. This is because of a proven theorem that says if whitestarts on any 2nx6 board, Black can at least get a tie by following these steps:1.If white plays A, B, E, or F, play directly on top of them2.If white plays C or D for the first time, play the opposing column3.If white plays C or D again, play directly on top of them For proof of threat theorems, see Victor Allis’ Thesis, “A Knowledge-BasedApproach of Connect-4, The Game is Solved: White Wins”.Deep Blue Deep Blue is a machine programmed by IBM to play chess. After six years ofprogramming Deep Blue, the IBM team felt that they were ready to challenge theworld champion - Gary Kasparov. In Game 1, 1996, Deep Blue started off with itsfirst win. But Kasparov learned quickly. He won the match four to two andconfidently proposed a rematch in 1997. Kasparov won the first game in a breeze.But the next game, Kasparov said, “It played differently, more strongly, unlike acomputer”. In the next three games, man and machine ended in a draw. Thenfinally, Deep Blue forced Kasparov into making a poor move. Kasparov resigned. Deep Blue used Brute Force, but the search looked past the first few moves.It challenged Kasparov with 256 processors that could search about 200 millionmoves per second. Deep Blue analyzed possible outcomes of the game.Grandmasters coached the programmers at IBM to deepen Deep Blue’s “book”,its library about how to win. Kasparov cannot try to use the Brute ForceApproach. Instead, he learns what is important from experience, and relies on thehuman mind’s ability to recognize patterns. The loss of Game 2 bore on Kasparov’s mind for the rest of the match. Aftergame 3, he quit. He was fed up. They had to convince him to get to the table toplay game 4 and game 5. “There was no game 6, because I didn’t want to play,” he
  17. 17. said. Although Deep Blue was smart, it did no think in the same way that humansdo. That is still many years and breakthroughs away. After the Deep Blue vs.Kasparov game IBM retired Deep Blue, and it never played again.TD-Gammon (Backgammon) Another use of AI in games is in backgammon. This was first used in theprogram BKG 9.8. This backgammon-playing program was made at CarnegieMelon University by Hans Berliner. In 1979, BKG 9.8 played a backgammonmatch against world champion Luigi Villa the day after he had won the worldchampionship in Monte Carlo. The stakes of the match were at 5,000$. Theprogram won with a final score of 7 to 1. Despite the score, Villa played betterthan BKG 9.8. He played almost all the right moves, while the backgammonprogram only play 65 out of 73 correct moves. Next in the 1980’s, Gerry Tesauro at IBM made a neural network program toplay backgammon. He called it Neurogammon. This program used encodedbackgammon knowledge in its memory of how to play. Neurogammon was alsoan expert system. After training on data sets of expert games, it could assignweights to the pieces of knowledge. The program was good enough to win the1989 Computer Olympiad. Tesauro’s next program used temporal difference learning, which meansthat instead of learning from games played by experts, it learns from self-playedgames. The program was called TD-Gammon (Temporal Difference-Gammon).The differences between TD-Gammon 0.0 and TD-Gammon 3.0 is a biggerneural net, more knowledge in the program, and smaller, more selective searches. TD-Gammon was one of the best backgammon players in the world. At theAAAI 98’ conference (Association for Advancement of Artificial IntelligenceConference 1998), TD-Gammon played the current world champion MalcolmDavis. To reduce the luck factor, the two players played 100 games over the span
  18. 18. of three days. In the end, Malcolm Davis won only by eight points. The neural netof the backgammon-playing program has 300 input values and contains 160hidden units. Approximately there were 50, 000 weights that were trained. To getTD-Gammon to its level at the AAAI conference, about 1, 500, 000 games had tobe played.Game Theory Game Theory is the branch of mathematics that deals with playing games. In Game Theory, a winning position is where you have a winning strategy,in which with a certain set of moves, you can win the game, no matter how wellyour opponent plays. A losing position is where your opponent has the winning strategy.Rule #1: From a winning position, you can get to a losing positionRule #2: From a losing position all the positions you can get to are winning Take the classic count to 10 problem: David and Wesley are playing a game.In the game, David starts. He can say one, two, or three consecutive numbers.Then Wesley goes. The game goes on. The person who says 10 loses. Does Davidhave a winning strategy? Answer: In this game, nine is the “obvious” losing position, because if you“receive” the number nine then you have lost. Therefore, eight, seven, and six areall winning positions, because you can get to nine. Five is losing, because you canonly get to six, seven, or eight, which are all winning positions. So four, three, andtwo are all winning positions, and one is losing. Therefore David’s winningstrategy is to say an amount of consecutive numbers such that on his first turn hestops at 1, on his second turn, 5, and his third turn, 9.Let’s try a harder problem: Ian and Larry are playing a game with 3 jars of marbles. On each player’s
  19. 19. turn, they must remove the same number of marbles from each of two differentjars. If a player is unable to do so, they lose the game (and their opponent wins). If it is Ian’s turn and the jars contain 2, 3, and 5 marbles respectively, whichplayer has a winning strategy? Just to make it easier: Any position with zero marbles in one jar or with twojars having the same amount of marbles in them is a winning position. This isbecause if there is one zero and two other numbers, your opponent will take awaythe same amount of marbles as there are in the jar with the least marbles, leavingyou with two zeros and no legal move, which is a win for them. And if there aretwo piles with the same amount of marbles, your opponent will make the twopiles have zero marbles, also leaving you with no legal move. Answer: For this problem, we can use a Game tree, or a Game Table. Ourgame tree (Fig. 5) will have the root branch equal to the current state. Since oursearch space is not unimaginably large, our successor nodes can be all possiblestates that we can get from this one. We can also represent this as a table. One of the many possible moves is to take two away from jar 1 and jar 2.What you can also is take two away from jar 1 and jar 3 or to take one marbleaway from jar 1 and jar 2. Since we proved that if we have one jar with no marblesin it, the position is a winning position, the first two options are both winning.Since we do not know if the third option is winning of losing, we have to gofurther. From 1/2/5, we can only get to: 0,1,5(W), 0,2,4(W), 1,1,4(W), 1,0,3(W),which are all winning positions. Therefore, 1/2/5 is a losing position. Here, we do not need to continue, because we have found out that 1/2/5 islosing by Rule #2, therefore that 2/3/5 is winning, by Rule #1. You can see thecomplete tree and table in Fig. 5.
  20. 20. 2/3/5(W) 0/1/5(W) 0/3/3(W) 1/2/5(L) 0/1/5(W) 0/2/4(W) 1/1/4(W) 1/0/3(W) Fig. 5 The tree and table. Notice that they are not complete because once we find out that 1/2/5 is losing, we know 2/3/5 is winningHere are some problems to do by yourself:a)Alphonse and Beryl are playing a game, starting with a pack of 52 cards. Alphonse begins by discarding at least one but not more than half of the cards in the pack. He then passes the remaining cards in the pack to Beryl. Beryl continues the game by discarding at least one but not more than half of the remaining cards in the pack. The game continues in this way with the pack being passed back and forth between the two players. The loser is the player who, at the beginning of his or her turn, receives only one card. Show, with justification, that there is always a winning strategy for Beryl.
  21. 21. b)(Hypatia ’03) Xavier and Yolanda are playing a game starting with some coins arranged in piles. Xavier always goes first, and the two players take turns removing one or more coins from any one pile. The player who takes the last coin wins. If there are two piles of coins with 3 coins in each pile, show that Yolanda can guarantee that she always wins the game.c)Alphonse and Beryl play a game by alternately moving a disk on a circular board. The game starts with the disk already on the board as shown. A player may move either clockwise one position or one position toward the centre but cannot move to a position that has been previously occupied. The last person who is able to move wins the game. (1) If Alphonse moves first, is there a strategy which guarantees that he will always win? (1)Is there a winning strategy for either of the players if the board is changed to five concentric circles with nine regions in each ring and Alphonse moves first? (The rules for playing this new game remain the same.)AI over timeTime LineIn the following section we describe the timeline depicted in Figure 6.•Analytical Engine: A Machine made by Charles Babbage in England. His machine could do “sixty additions or subtractions may be completed and printed in one minute. One multiplication of two numbers, each of fifty figures, in one minute. One division of a number having 100 places of figures by another of 50 can be printed in one minute.” Although Babbage spent 40 years doing this, he could not afford to finish because the technology of the 19th century was not advanced enough.•First Computer Program: The Countess of Lovelace realized that Babbage’s Analytical Engine could take instructions by punching holes in cards.
  22. 22. •Binary Logic: Also called Boolean Logic. The point of Boolean Logic is to represent a function of a logic gate (Logic gates process signals that are either true or false which can also be shown as 1 and 0), and this can be shown in a truth table. In binary logic, the rules are as follows: NOT gate: The Output Q is true when the input A is NOT true (false) AND gate: The output Q is true if A and B are true NAND gate (NOT AND): The output is true if A and B are NOT true OR gate: The output Q is true if A OR B is true NOR (NOT OR) gate: The output is true if A OR B is NOT true•The Automatic Totalizator: This was invented for tallying up bets for horse races. The first Automatic Totalizator was so big, it needed its own building!•The Colossus Computer: This was invented for cracking the German codes called enigma during World War 2. The British teamed up to do this with the Polish.•The Commercial Magnetic Memory Computer: A computer that used magnetic memory.•Commercial Robotics: Unimation started making commercial robots•Personal Computer: The first PC•CD-ROM: The first CD-ROM•Lightweight laptop: This laptop weighed less than two pounds!!Predictions First of all, I would like to clarify that these are all my predictions, and arebased on what many other scientists think. These are not all proven to be correctby any means•Security recognition: The ability for a machine to recognize faces. This is one of
  23. 23. humanity’s current strengths over AI.•Household Chores: AI operated robots will be able to wash dishes, control air conditioning, do the laundry, etc.•Nano-Technology: Tiny AI-controlled robots, will be used for traveling in human blood stream, and keeping things clean. These robots are no bigger than the width of a human hair.•AI Controlled Space Ship: By the end of these 35 years, planes and space ships will be able to navigate in the space autonomously.•Virtual Surgery: Surgeons will be using virtual reality (see Robotics), to perform surgeries in other countries.•AI surpasses human intelligence: Most scientists think sooner than this prediction. But Dr. Rodney Brooks argued and compared what we know about AI now to what people knew about the solar system 500 years ago. Back then, they knew that the planets moved, but they did not know why. We still do not know some basic things about AI.Predicted Future for AI So far, our predictions for AI have not been very accurate. For example,scientists predicted that the world chess champion would be beaten in a matchagainst a machine in the year 1968, while the first time that happened wasactually in 1997, about 30 years off. However, AI researchers are still optimisticabout its future. For example, there is a prediction that by 2050, everything willuse AI in some way, although some researchers argue that this is already inplace. Fuel injection systems for cars use learning algorithms. Jet turbines usegenetic algorithms. More examples are email, cellphones, X-ray reading systems,and systems that book airplane flights. According to Dr. Rodney Brooks, thedirector of the Massachusetts Institute of Technology’s Artificial Intelligence lab,
  24. 24. our research position and knowledge of AI is about the same as the state ofPersonal Computers in 1978. Ray Kurzweil, the author of two AI books, The Ageof Spiritual Machines and The Age of Intelligent Machines, says that popularintelligent machines like HAL, Commander Data in Star Trek, and David in thefilm AI are not very far away. Dr. Brooks believes that by 2030, we will have thebasic template of intelligence. Then, Dr. Brooks reminded, “who thought that by2001, you would have four computers in your kitchen?” pointing to the computerchips in your fridge, coffee makers, stoves and radios.ConclusionIn conclusion, Artificial Intelligence will surpass human intelligence. Although ithas proven itself to be similar to the human brain, computers do not think in thesame way. There have been many problems found, and their solutions are still afew years away. Nevertheless, AI has had some strength over humanity, and thefuture of AI remains uncertain. In this report, we have discussed applications ofAI and their impact on our lives. AI games provide entertainment, introduce newalgorithms, and give a challenge, not only to its human opponent; but to otherArtificial Intelligence programmers too.Bibliography/Works CitedBooksMargulies, Philip. Artificial Intelligence. Michigan: Blackbirch Press, 2004Graham, I., Gwynn-Jones, T., Lynch, A., Parker, S., & Wood, R. Science. Australia:! Weldon Owen, 2001Jefferis, David. Artificial Intelligence, Machine Evolution and Robotics. St. Catharineʼs,
  25. 25. ! Canada: Crabtree, 1999Hyland, Tony. How Robots Work. Minnesota: Smart Apple Media, 2007Flanagan, David. Java in a Nutshell. Sebastopol: OʼReilly, 1996-97Barr, Avron & Fiegenbaum A., Edward. The Handbook of Artificial Intelligence VolumeOne. Stanford: William Krauford, Inc., 1981Smith, Raoul. Artificial Intelligence. New York: Facts on File, Inc., 1989Crevier, Daniel. AI: The Tumultuous History of the Search for Artificial Intelligence. New! York: BasicBooks, 1993Levitin, Anany. Introduction to Design & Analysis of Algorithms. City Unkown: Pearson! Addison-Wesley, 2007Magazine/Newspaper ArticlesSchaeffer, Jonathan, “A Gamut of Games.” AI Magazine. Vol. 22 No. 3, (Fall 2001):! 29-46.Anderson, Kevin(2001, September 21). Predicting AIʼs Future. BBC News. Retrieved! from http://bit.ly/bvgLJRVideosDeep Blue Beat G. Kasparov in 1997. Eustake, Youtube, 2007. URL: http://bit.ly/bbY6b0Game Over: Kasparov vs. Machine. argishtib, Youtube, 2007. URL: http://bit.ly/cZXE4IWebsitesHonda. http://asimo.honda.com/InsideAsimo.aspx. Honda Motor Co. Inc., 2010University of Waterloo Faculty of Mathematics. http://www.cemc.uwaterloo.ca/events/mathcircles/2009-10/Senior_Feb3.pdf. CEMC, 2010University of Waterloo Faculty of Mathematics. http://www.cemc.uwaterloo.ca/events/mathcircles/2009-10/Senior_Feb10.pdf. CEMC, 2010University of Waterloo Faculty of Mathematics. http://www.cemc.uwaterloo.ca/events/mathcircles/2009-10/Senior_Feb17.pdf. CEMC, 2010[1] Author Unknown. http://www.its.bldrdoc.gov/fs-1037/dir-003/_0371.htm. 1996
  26. 26. McCarthy, John. http://www-formal.stanford.edu/jmc/whatisai/node1.html. Stanford,! 2007Rudnik, John. http://www.math.ca/Competitions/COMC/. Canadian Mathematical! Society, 2010CEMC. http://bit.ly/af7gGI. University of Waterloo, 2010Hewes, John. http://www.kpsec.freeuk.com/gates.htm#nand. The Electronics Club,! 2010Powerhouse Museum. http://bit.ly/b4alxY. The Australian Academy of Technological! Sciences and EngineeringAuthor Unknown. http://didyouknow.org/ai/. Did You Know, 2010Research PapersBertoletti, G. (1997). Connect-4 [Data file]. Retrieved from http://pd-resource.net/! Connect-4/Velena/PicturesPaone, Joe.http://castercomm.files.wordpress.com/2009/10/binary.jpg. Wordpress, 2009Allis, Victor. A Knowledge-Based Approach to Connect 4. http://www.connectfour.net/Files/connect4.pdf, 1998.Ogden, Sam. http://web.mit.edu/museum/img/exhibitions/Kismet_312.jpg. MIT, 2008Honda. http://bit.ly/abfTcR. Honda Motor Co. Inc., 2010Author Unknown.http://bit.ly/14kDB8. IBM, Year UnknownPeiretti, Federico. http://bit.ly/97dxHz. TuttoLibri, 2007Robers, Eric S. The Art and Science of C. Addison-Wesley Publishing Company, 2005CBS Interactive. http://news.cnet.com/2300-11386_3-6084282.html. cnet news, 2010

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