Artificial Intelligence

Transcription

1 Artificial Intelligence Chapter 1 Chapter 1 1

2 Outline Course overview What is AI? A brief history The state of the art Chapter 1 2

3 intelligent agents search and game-playing logical systems planning systems Course overview uncertainty probability and decision theory learning language perception robotics philosophical issues Chapter 1 3

4 What is AI? Systems that think like humans Systems that think rationally Systems that act like humans Systems that act rationally Chapter 1 4

5 Acting humanly: The Turing test Turing (1950) Computing machinery and intelligence : Can machines think? Can machines behave intelligently? Operational test for intelligent behavior: the Imitation Game HUMAN HUMAN INTERROGATOR? AI SYSTEM Predicted that by 2000, a machine might have a 30% chance of fooling a lay person for 5 minutes Anticipated all major arguments against AI in following 50 years Suggested major components of AI: knowledge, reasoning, language understanding, learning Problem: Turing test is not reproducible, constructive, or amenable to mathematical analysis Chapter 1 5

6 Thinking humanly: Cognitive Science 1960s cognitive revolution : information-processing psychology replaced prevailing orthodoxy of behaviorism Requires scientific theories of internal activities of the brain What level of abstraction? Knowledge or circuits? How to validate? Requires 1) Predicting and testing behavior of human subjects (top-down) or 2) Direct identification from neurological data (bottom-up) Both approaches (roughly, Cognitive Science and Cognitive Neuroscience) are now distinct from AI Both share with AI the following characteristic: the available theories do not explain (or engender) anything resembling human-level general intelligence Hence, all three fields share one principal direction! Chapter 1 6

7 Thinking rationally: Laws of Thought Normative (or prescriptive) rather than descriptive Aristotle: what are correct arguments/thought processes? Several Greek schools developed various forms of logic: notation and rules of derivation for thoughts; may or may not have proceeded to the idea of mechanization Direct line through mathematics and philosophy to modern AI Problems: 1) Not all intelligent behavior is mediated by logical deliberation 2) What is the purpose of thinking? What thoughts should I have? Chapter 1 7

8 Acting rationally Rational behavior: doing the right thing The right thing: that which is expected to maximize goal achievement, given the available information Doesn t necessarily involve thinking e.g., blinking reflex but thinking should be in the service of rational action Aristotle (Nicomachean Ethics): Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good Chapter 1 8

9 Rational agents An agent is an entity that perceives and acts This course is about designing rational agents Abstractly, an agent is a function from percept histories to actions: f : P A For any given class of environments and tasks, we seek the agent (or class of agents) with the best performance Caveat: computational limitations make perfect rationality unachievable design best program for given machine resources Chapter 1 9

10 Philosophy Mathematics Psychology Economics Linguistics AI prehistory logic, methods of reasoning mind as physical system foundations of learning, language, rationality formal representation and proof algorithms, computation, (un)decidability, (in)tractability probability adaptation phenomena of perception and motor control experimental techniques (psychophysics, etc.) formal theory of rational decisions knowledge representation grammar Neuroscience Control theory homeostatic systems, stability simple optimal agent designs plastic physical substrate for mental activity Chapter 1 10

11 Potted history of AI 1943 McCulloch & Pitts: Boolean circuit model of brain 1950 Turing s Computing Machinery and Intelligence Look, Ma, no hands! 1950s Early AI programs, including Samuel s checkers program, Newell & Simon s Logic Theorist, Gelernter s Geometry Engine 1956 Dartmouth meeting: Artificial Intelligence adopted 1965 Robinson s complete algorithm for logical reasoning AI discovers computational complexity Neural network research almost disappears Early development of knowledge-based systems Expert systems industry booms Expert systems industry busts: AI Winter Neural networks return to popularity 1988 Resurgence of probability; general increase in technical depth Nouvelle AI : ALife, GAs, soft computing 1995 Agents agents everywhere... Chapter 1 11

12 State of the art Which of the following can be done at present? Play a decent game of table tennis Drive along a curving mountain road Drive in the center of Cairo Buy a week s worth of groceries at Berkeley Bowl Buy a week s worth of groceries on the web Play a decent game of bridge Discover and prove a new mathematical theorem Write an intentionally funny story Give competent legal advice in a specialized area of law Translate spoken English into spoken Swedish in real time Perform a complex surgical operation Chapter 2 12

13 Intelligent Agents Chapter 2 Chapter 2 13

14 Outline Agents and environments Rationality PEAS (Performance measure, Environment, Actuators, Sensors) Environment types Agent types Chapter 2 14

15 Agents and environments sensors environment percepts actions? agent actuators Agents include humans, robots, softbots, thermostats, etc. The agent function maps from percept histories to actions: f : P A The agent program runs on the physical architecture to produce f Chapter 2 15

16 Vacuum-cleaner world A B Percepts: location and contents, e.g., [A, Dirty] Actions: Left, Right, Suck, NoOp Chapter 2 16

17 A vacuum-cleaner agent Percept sequence Action [A, Clean] Right [A, Dirty] Suck [B, Clean] Lef t [B, Dirty] Suck [A, Clean], [A, Clean] Right [A, Clean], [A, Dirty]. Suck. function Reflex-Vacuum-Agent( [location,status]) returns an action if status = Dirty then return Suck else if location = A then return Right else if location = B then return Left What is the right function? Can it be implemented in a small agent program? Chapter 2 17

18 Rationality Fixed performance measure evaluates the environment sequence one point per square cleaned up in time T? one point per clean square per time step, minus one per move? penalize for > k dirty squares? A rational agent chooses whichever action maximizes the expected value of the performance measure given the percept sequence to date Rational omniscient Rational clairvoyant Rational successful Rational exploration, learning, autonomy Chapter 2 18

19 PEAS To design a rational agent, we must specify the task environment Consider, e.g., the task of designing an automated taxi: Performance measure?? Environment?? Actuators?? Sensors?? Chapter 2 19

20 PEAS To design a rational agent, we must specify the task environment Consider, e.g., the task of designing an automated taxi: Performance measure?? safety, destination, profits, legality, comfort,... Environment?? US streets/freeways, traffic, pedestrians, weather,... Actuators?? steering, accelerator, brake, horn, speaker/display,... Sensors?? video, accelerometers, gauges, engine sensors, keyboard, GPS,... Chapter 2 20

21 Performance measure?? Environment?? Actuators?? Sensors?? Internet shopping agent Chapter 2 21

22 Environment types Observable?? Deterministic?? Episodic?? Static?? Discrete?? Single-agent?? Solitaire Backgammon Internet shopping Taxi Chapter 2 22

23 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Episodic?? Static?? Discrete?? Single-agent?? Chapter 2 23

24 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Yes No Partly No Episodic?? Static?? Discrete?? Single-agent?? Chapter 2 24

25 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Yes No Partly No Episodic?? No No No No Static?? Discrete?? Single-agent?? Chapter 2 25

26 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Yes No Partly No Episodic?? No No No No Static?? Yes Semi Semi No Discrete?? Single-agent?? Chapter 2 26

27 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Yes No Partly No Episodic?? No No No No Static?? Yes Semi Semi No Discrete?? Yes Yes Yes No Single-agent?? Chapter 2 27

28 Environment types Solitaire Backgammon Internet shopping Taxi Observable?? Yes Yes No No Deterministic?? Yes No Partly No Episodic?? No No No No Static?? Yes Semi Semi No Discrete?? Yes Yes Yes No Single-agent?? Yes No Yes (except auctions) No The environment type largely determines the agent design The real world is (of course) partially observable, stochastic, sequential, dynamic, continuous, multi-agent Chapter 2 28

29 Agent types Four basic types in order of increasing generality: simple reflex agents reflex agents with state goal-based agents utility-based agents All these can be turned into learning agents Chapter 2 29

30 Simple reflex agents Agent Sensors Condition action rules What the world is like now What action I should do now Environment Actuators Chapter 2 30

31 Reflex agents with state State How the world evolves What my actions do Condition action rules Sensors What the world is like now What action I should do now Environment Agent Actuators Chapter 2 31

32 Goal-based agents State How the world evolves What my actions do Goals Sensors What the world is like now What it will be like if I do action A What action I should do now Environment Agent Actuators Chapter 2 32

33 Utility-based agents State How the world evolves What my actions do Utility Sensors What the world is like now What it will be like if I do action A How happy I will be in such a state What action I should do now Environment Agent Actuators Chapter 2 33

34 Performance standard Learning agents Critic Sensors feedback learning goals Learning element changes knowledge Performance element Environment Problem generator Agent Actuators Chapter 3, Sections

35 Problem solving and search Chapter 3, Sections 1 5 Chapter 3, Sections

36 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Chapter 3, Sections

37 Restricted form of general agent: Problem-solving agents function Simple-Problem-Solving-Agent( percept) returns an action static: seq, an action sequence, initially empty state, some description of the current world state goal, a goal, initially null problem, a problem formulation state Update-State(state, percept) if seq is empty then goal Formulate-Goal(state) problem Formulate-Problem(state, goal) seq Search( problem) action Recommendation(seq, state) seq Remainder(seq, state) return action Note: this is offline problem solving; solution executed eyes closed. Online problem solving involves acting without complete knowledge. Chapter 3, Sections

38 Example: Romania On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest Formulate goal: be in Bucharest Formulate problem: states: various cities actions: drive between cities Find solution: sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest Chapter 3, Sections

39 71 Oradea Example: Romania Neamt Zerind 75 Arad Timisoara Dobreta 151 Sibiu 99 Fagaras 80 Rimnicu Vilcea Lugoj Mehadia 120 Pitesti Bucharest Craiova 90 Giurgiu 87 Iasi Urziceni Vaslui Hirsova 86 Eforie Chapter 3, Sections

40 Problem types Deterministic, fully observable = single-state problem Agent knows exactly which state it will be in; solution is a sequence Non-observable = conformant problem Agent may have no idea where it is; solution (if any) is a sequence Nondeterministic and/or partially observable = contingency problem percepts provide new information about current state solution is a tree or policy often interleave search, execution Unknown state space = exploration problem ( online ) Chapter 3, Sections

41 Example: vacuum world Single-state, start in #5. Solution?? Chapter 3, Sections

42 Example: vacuum world Single-state, start in #5. Solution?? [Right, Suck] Conformant, start in {1, 2, 3, 4, 5, 6, 7, 8} e.g., Right goes to {2, 4, 6, 8}. Solution?? Chapter 3, Sections

43 Example: vacuum world Single-state, start in #5. Solution?? [Right, Suck] Conformant, start in {1, 2, 3, 4, 5, 6, 7, 8} e.g., Right goes to {2, 4, 6, 8}. Solution?? [Right, Suck, Lef t, Suck] Contingency, start in #5 Murphy s Law: Suck can dirty a clean carpet Local sensing: dirt, location only. Solution?? Chapter 3, Sections

44 Example: vacuum world Single-state, start in #5. Solution?? [Right, Suck] Conformant, start in {1, 2, 3, 4, 5, 6, 7, 8} e.g., Right goes to {2, 4, 6, 8}. Solution?? [Right, Suck, Lef t, Suck] Contingency, start in #5 Murphy s Law: Suck can dirty a clean carpet Local sensing: dirt, location only. Solution?? [Right, if dirt then Suck] Chapter 3, Sections

45 Single-state problem formulation A problem is defined by four items: initial state e.g., at Arad successor function S(x) = set of action state pairs e.g., S(Arad) = { Arad Zerind, Zerind,...} goal test, can be explicit, e.g., x = at Bucharest implicit, e.g., N odirt(x) path cost (additive) e.g., sum of distances, number of actions executed, etc. c(x, a, y) is the step cost, assumed to be 0 A solution is a sequence of actions leading from the initial state to a goal state Chapter 3, Sections

46 Selecting a state space Real world is absurdly complex state space must be abstracted for problem solving (Abstract) state = set of real states (Abstract) action = complex combination of real actions e.g., Arad Zerind represents a complex set of possible routes, detours, rest stops, etc. For guaranteed realizability, any real state in Arad must get to some real state in Zerind (Abstract) solution = set of real paths that are solutions in the real world Each abstract action should be easier than the original problem! Chapter 3, Sections

47 Example: vacuum world state space graph L R L R S S L R R L R R L L S S S S L R L R S S states?? actions?? goal test?? path cost?? Chapter 3, Sections

48 Example: vacuum world state space graph R L S S S S R L R L R L S S S S L L L L R R R R states??: integer dirt and robot locations (ignore dirt amounts) actions??: Left, Right, Suck, NoOp goal test??: no dirt path cost??: 1 per action (0 for NoOp) Chapter 3, Sections

49 Example: The 8-puzzle Start State Goal State states?? actions?? goal test?? path cost?? Chapter 3, Sections

50 Example: The 8-puzzle Start State Goal State states??: integer locations of tiles (ignore intermediate positions) actions??: move blank left, right, up, down (ignore unjamming etc.) goal test??: = goal state (given) path cost??: 1 per move [Note: optimal solution of n-puzzle family is NP-hard] Chapter 3, Sections

51 Example: robotic assembly P R R R R R states??: real-valued coordinates of robot joint angles parts of the object to be assembled actions??: continuous motions of robot joints goal test??: complete assembly with no robot included! path cost??: time to execute Chapter 3, Sections

52 Tree search algorithms Basic idea: offline, simulated exploration of state space by generating successors of already-explored states (a.k.a. expanding states) function Tree-Search( problem, strategy) returns a solution, or failure initialize the search tree using the initial state of problem loop do if there are no candidates for expansion then return failure choose a leaf node for expansion according to strategy if the node contains a goal state then return the corresponding solution else expand the node and add the resulting nodes to the search tree end Chapter 3, Sections

53 Tree search example Arad Sibiu Timisoara Zerind Arad Fagaras Oradea Rimnicu Vilcea Arad Lugoj Arad Oradea Chapter 3, Sections

54 Tree search example Arad Sibiu Timisoara Zerind Arad Fagaras Oradea Rimnicu Vilcea Arad Lugoj Arad Oradea Chapter 3, Sections

55 Tree search example Arad Sibiu Timisoara Zerind Arad Fagaras Oradea Rimnicu Vilcea Arad Lugoj Arad Oradea Chapter 3, Sections

56 Implementation: states vs. nodes A state is a (representation of) a physical configuration A node is a data structure constituting part of a search tree includes parent, children, depth, path cost g(x) States do not have parents, children, depth, or path cost! parent, action State Node depth = 6 g = state The Expand function creates new nodes, filling in the various fields and using the SuccessorFn of the problem to create the corresponding states. Chapter 3, Sections

57 Implementation: general tree search function Tree-Search( problem, fringe) returns a solution, or failure fringe Insert(Make-Node(Initial-State[problem]), fringe) loop do if fringe is empty then return failure node Remove-Front(fringe) if Goal-Test[problem] applied to State(node) succeeds return node fringe InsertAll(Expand(node, problem), fringe) function Expand( node, problem) returns a set of nodes successors the empty set for each action, result in Successor-Fn[problem](State[node]) do s a new Node Parent-Node[s] node; Action[s] action; State[s] result Path-Cost[s] Path-Cost[node] + Step-Cost(node, action, s) Depth[s] Depth[node] + 1 add s to successors return successors Chapter 3, Sections

58 Search strategies A strategy is defined by picking the order of node expansion Strategies are evaluated along the following dimensions: completeness does it always find a solution if one exists? time complexity number of nodes generated/expanded space complexity maximum number of nodes in memory optimality does it always find a least-cost solution? Time and space complexity are measured in terms of b maximum branching factor of the search tree d depth of the least-cost solution m maximum depth of the state space (may be ) Chapter 3, Sections

59 Uninformed search strategies Uninformed strategies use only the information available in the problem definition Breadth-first search Uniform-cost search Depth-first search Depth-limited search Iterative deepening search Chapter 3, Sections

60 Expand shallowest unexpanded node Breadth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end A B C D E F G Chapter 3, Sections

61 Expand shallowest unexpanded node Breadth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end A B C D E F G Chapter 3, Sections

62 Expand shallowest unexpanded node Breadth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end A B C D E F G Chapter 3, Sections

63 Expand shallowest unexpanded node Breadth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end A B C D E F G Chapter 3, Sections

64 Properties of breadth-first search Complete?? Chapter 3, Sections

65 Properties of breadth-first search Complete?? Yes (if b is finite) Time?? Chapter 3, Sections

66 Properties of breadth-first search Complete?? Yes (if b is finite) Time?? 1 + b + b 2 + b b d + b(b d 1) = O(b d+1 ), i.e., exp. in d Space?? Chapter 3, Sections

67 Properties of breadth-first search Complete?? Yes (if b is finite) Time?? 1 + b + b 2 + b b d + b(b d 1) = O(b d+1 ), i.e., exp. in d Space?? O(b d+1 ) (keeps every node in memory) Optimal?? Chapter 3, Sections

68 Properties of breadth-first search Complete?? Yes (if b is finite) Time?? 1 + b + b 2 + b b d + b(b d 1) = O(b d+1 ), i.e., exp. in d Space?? O(b d+1 ) (keeps every node in memory) Optimal?? Yes (if cost = 1 per step); not optimal in general Space is the big problem; can easily generate nodes at 10MB/sec so 24hrs = 860GB. Chapter 3, Sections

69 Expand least-cost unexpanded node Uniform-cost search Implementation: fringe = queue ordered by path cost Equivalent to breadth-first if step costs all equal Complete?? Yes, if step cost ɛ Time?? # of nodes with g cost of optimal solution, O(b C /ɛ ) where C is the cost of the optimal solution Space?? # of nodes with g cost of optimal solution, O(b C /ɛ ) Optimal?? Yes nodes expanded in increasing order of g(n) Chapter 3, Sections

70 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

71 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

72 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

73 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

74 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

75 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

76 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

77 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

78 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

79 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

80 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

81 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front A B C D E F G H I J K L M N O Chapter 3, Sections

82 Properties of depth-first search Complete?? Chapter 3, Sections

83 Properties of depth-first search Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces Time?? Chapter 3, Sections

84 Properties of depth-first search Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces Time?? O(b m ): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first Space?? Chapter 3, Sections

85 Properties of depth-first search Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces Time?? O(b m ): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first Space?? O(bm), i.e., linear space! Optimal?? Chapter 3, Sections

86 Properties of depth-first search Complete?? No: fails in infinite-depth spaces, spaces with loops Modify to avoid repeated states along path complete in finite spaces Time?? O(b m ): terrible if m is much larger than d but if solutions are dense, may be much faster than breadth-first Space?? O(bm), i.e., linear space! Optimal?? No Chapter 3, Sections

87 Depth-limited search = depth-first search with depth limit l, i.e., nodes at depth l have no successors Recursive implementation: function Depth-Limited-Search( problem, limit) returns soln/fail/cutoff Recursive-DLS(Make-Node(Initial-State[problem]), problem, limit) function Recursive-DLS(node, problem, limit) returns soln/fail/cutoff cutoff-occurred? false if Goal-Test[problem](State[node]) then return node else if Depth[node] = limit then return cutoff else for each successor in Expand(node, problem) do result Recursive-DLS(successor, problem, limit) if result = cutoff then cutoff-occurred? true else if result failure then return result if cutoff-occurred? then return cutoff else return failure Chapter 3, Sections

88 Iterative deepening search function Iterative-Deepening-Search( problem) returns a solution inputs: problem, a problem for depth 0 to do result Depth-Limited-Search( problem, depth) if result cutoff then return result end Chapter 3, Sections

89 Iterative deepening search l = 0 Limit = 0 A A Chapter 3, Sections

90 Iterative deepening search l = 1 Limit = 1 A A A A B C B C B C B C Chapter 3, Sections

91 Iterative deepening search l = 2 Limit = 2 A A A A B C B C B C B C D E F G D E F G D E F G D E F G A A A A B C B C B C B C D E F G D E F G D E F G D E F G Chapter 3, Sections

92 Iterative deepening search l = 3 Limit = 3 A A A A B C B C B C B C D E F G D E F G D E F G D E F G H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O A A A A B C B C B C B C D E F G D E F G D E F G D E F G H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O A A A A B C B C B C B C D E F G D E F G D E F G D E F G H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O Chapter 3, Sections

93 Complete?? Properties of iterative deepening search Chapter 3, Sections

94 Properties of iterative deepening search Complete?? Yes Time?? Chapter 3, Sections

95 Properties of iterative deepening search Complete?? Yes Time?? (d + 1)b 0 + db 1 + (d 1)b b d = O(b d ) Space?? Chapter 3, Sections

96 Properties of iterative deepening search Complete?? Yes Time?? (d + 1)b 0 + db 1 + (d 1)b b d = O(b d ) Space?? O(bd) Optimal?? Chapter 3, Sections

97 Properties of iterative deepening search Complete?? Yes Time?? (d + 1)b 0 + db 1 + (d 1)b b d = O(b d ) Space?? O(bd) Optimal?? Yes, if step cost = 1 Can be modified to explore uniform-cost tree Numerical comparison for b = 10 and d = 5, solution at far right: N(IDS) = , , , 000 = 123, 450 N(BFS) = , , , , 990 = 1, 111, 100 Chapter 3, Sections

98 Summary of algorithms Criterion Breadth- Uniform- Depth- Depth- Iterative First Cost First Limited Deepening Complete? Yes Yes No Yes, if l d Yes Time b d+1 b C /ɛ b m b l b d Space b d+1 b C /ɛ bm bl bd Optimal? Yes Yes No No Yes Chapter 3, Sections

99 Repeated states Failure to detect repeated states can turn a linear problem into an exponential one! A A B B B C C C C C D Chapter 3, Sections

100 Graph search function Graph-Search( problem, fringe) returns a solution, or failure closed an empty set fringe Insert(Make-Node(Initial-State[problem]), fringe) loop do if fringe is empty then return failure node Remove-Front(fringe) if Goal-Test[problem](State[node]) then return node if State[node] is not in closed then add State[node] to closed fringe InsertAll(Expand(node, problem), fringe) end Chapter 3, Sections

101 Summary Problem formulation usually requires abstracting away real-world details to define a state space that can feasibly be explored Variety of uninformed search strategies Iterative deepening search uses only linear space and not much more time than other uninformed algorithms Chapter 3, Sections