Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found

Transcription

1

2 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found Example: Find a route from Tasi to Arad A simplified map of Romania (taken from AIMA, Russel&Norvig)

3 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found Example: Find a route from Tasi to Arad State: location ( at Sibiu ) Connections: neighboring locations Current state: at Tasi Goal state: at Arad

4 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found This is done by building a search tree at Tasi 1

5 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found This is done by building a search tree at Tasi 1 at Neamt at Vaslui

6 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found This is done by building a search tree at Tasi 1 at Neamt at Vaslui 2

7 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found This is done by building a search tree at Tasi 1 at Neamt at Vaslui 2 at Tasi at Urziceni

8 Searching Tools Search = the exploration of a search space, which is a collection of search states and connections between them, until a goal state is found This is done by building a search tree Building the search tree is searching Different strategies of selecting the next state for building the search tree correspond to different types of search (e.g. breadth first, depth first,..) Several nodes in the search tree can point to the same state in search space ( repeated states )

9 Searching Tools Current state (where we currently are at) Successor function (where we can go from there) Goal test function (are we at the goal state?) Queue or fringe of tree frontier A strategy to select the next current state from the fringe at Tasi 1 at Neamt at Vaslui 2 at Tasi at Urziceni Problem Solution

10 Searching Tools Current state (where we currently are at) Successor function (where we can go from there) Goal test function (are we at the goal state?) Queue or fringe of tree frontier A strategy to select the next current state from the fringe

11 Searching Tools Example 1: Depth first search? Example 2: Breadth first search?

12 Searching Tools Example 1: Depth first search Example 2: Breadth first search

13 Requires extra information, e.g. straight line distance between locations Then we not append or prepend new states to states, but sort them according to how promising they look Extra information: Straight-line distance to goal (Bucharest)

14 Requires extra information, e.g. straight line distance between locations Then we not append or prepend new states to states, but sort them according to how promising they look

15 Properties of the search strategies Completeness (is a solution always found?) Optimality (is the best solution found first, e.g. the shortest path?) Time complexity e.g. in terms of branching factor b and the solution depth d, and the max tree depth m Space complexity Breadth First Depth First Complete??? Optimal??? Time Complexity?? Space Complexity??

16 Properties of the search strategies Completeness (is a solution always found?) Optimality (is the best solution found first, e.g. the shortest path?) Time complexity e.g. in terms of branching factor b and the solution depth d, and the max tree depth m Space complexity Breadth First Complete? Optimal? Time Complexity Space Complexity Exponential!! YES YES, if each action has equal cost b+b2+...+bd = O(bd) O(bd) Depth First YES, if finite search tree NO O(bm) O(bm)

17 In between breadth-first and depth first: Beam Search Notice: - If beam-width = infinity best-first search - If beam-width = 1 depth-first search without backup or hill climbing

18 An Example: planning a trip...

19 An Example: planning a trip...

20 An Example: planning a trip...

21 San Francisco Denver rg h Pi tts bu Kansas city In di Reno Grand Junction an ap o lis An Example: planning a trip... Boston

22 An Example: planning a trip... and back

23 San Francisco Flagstaff Denver rg h lis an ap o Kansas city Pi tts bu Reno Grand Junction In di C hi ca g o An Example: planning a trip...and back Boston

24 Denver rg h lis an ap o Kansas city Pi tts bu Reno Grand Junction In di C hi ca g o An Example: planning a trip...and back San Francisco Flagstaff => Instead of minimizing the (estimated) distance left to travel, we should minimize the (estimates) total distance i.e. distance traveled so far + (estimated) left to travel Boston

25 Minimizing the total (estimated) distance Consider again:

26 Minimizing the total (estimated) distance Consider again: => we can keep cost information in a state data structure provided that the functions Goal-p, successors and cost-fn are modified to work on state data structure

27 Good choice: states as nodes in the search tree (= paths): Then we turn the successors function into a function that works on paths and returns a list of paths instead of ordinary states :

28 => minimizing the total (estimated) distance

29 Specializing search So far, all search strategies were built upon tree-search Almost anything can be represented as a tree However, often advantage can (and should) be taken of additional structure in the search space Example: graph search Some nodes in the search tree point to the same search space state Huge pruning opportunities possible by checking for repeated states

30

31 graph search with paths = A* search If a successor state already occurs in states or in old-states, keep only the best (lowest cost) state in states => requires lookup of states in paths, comparing paths and addition and deletion of paths

32 (defun a*-search (paths goal-p successors cost-fn cost-left-fn &optional (state= #'eql) old-paths) (cond ((null paths) fail) ((funcall goal-p (path-state (first paths))) (first paths)) (t (let* ((path (pop paths)) (state (path-state path))) (setf old-paths (insert-path path old-paths)) (dolist (state2 (funcall successors state)) (let* ((cost (+ (path-cost-so-far path) (funcall cost-fn state state2))) (cost2 (funcall cost-left-fn state2)) (path2 (make-path :state state2 :previous path :cost-so-far cost :total-cost (+ cost cost2))) (old nil)) (cond ((setf old (find-path state2 paths state=)) (when (better-path path2 old) (setf paths (insert-path path2 (delete old paths))))) ((setf old (find-path state2 old-paths state=)) (when (better-path path2 old) (setf paths (insert-path path2 paths)) (setf old-paths (delete old old-paths)))) (t (setf paths (insert-path path2 paths)))))) (a*-search paths goal-p successors cost-fn cost-left-fn state= old-paths)))))

33 The 3-block's world search space

34 Recall: (defun GPS (state goals &optional (*ops* *ops*)) "General Problem Solver: from state, achieve goals using *ops*." (find-all-if #'action-p (achieve-all (cons '(start) state) goals nil))) State is a list of predicates Goal is achieved if goals is a subset of the state As a cost function we can take the number of actions taken so far plus the number of unsatisfied predicates

35

36

37 GPS as search easily solves the Sussman anomaly: Note: Now we search forward from the start state to the goal state Question: How could means-ends analysis be implemented as search?

38

39 Eliza Developed by Joseph Weizenbaum in 1965 Note: Now we search forward from the start state to the goal state Question: How could means-ends analysis be implemented as search?

40 Eliza Developed by Joseph Weizenbaum in 1965 One of the first programs to feature English output and input Named after the heroine of Pygmalion, who fooled others into believing she was upper class after being taught proper English by a professor Example dialogue (Eliza output in capitals):

41 Eliza Appears to show exhibit true understanding, but this is an illusion: It is merely recognizing, transforming and echoing pieces of the input E.g.: When given the word same or alike, it outputs a question about similarity When given an input I need X, it outputs What would it mean to you if you got X

42 Eliza Appears to show exhibit true understanding, but this is an illusion: It is merely recognizing, transforming and echoing pieces of the input E.g.: When given the word same or alike, it outputs a question about similarity When given an input I need X, it outputs What would it mean to you if you got X When given the input I need this like a whole in the head, Eliza responds with What would it mean to you if you got this like a whole in the head? Eliza programmed to simulate a psychotherapist Parry programmed to simulate Paranoid behavior

43 Programming Eliza (1) Read input (2) Find a pattern that matches the input (3) Transform the pattern to a response (4) Print the response

44 Programming Eliza (1) Read input (read list-of-symbols) (2) Find a pattern that matches the input

45 Programming Eliza (1) Read input (read list-of-symbols) (2) Find a pattern that matches the input Match i with i, need with need etc.:

46 Variables and bindings

47 Variables and bindings OK, but we will also need the variable bindings in the transformation: Exercise: search the 5 (!) bugs in the above function

48 Variables and bindings (eql pattern input) may return T, which is not a list NIL indicates both failure and success with no bindings The case of failure should be caught (and not just appended) If a variable appears several times in the pattern, the bindings should match 5. If the first doesn't match, the rest should not be cheched anymore

49 Variables and bindings

50 Variables and bindings

51 Variables and bindings

52

53

54

55 Programming Eliza (1) Read input (read list-of-words) (2) Find a pattern that matches the input (3) Transform the pattern to a response

56 Programming Eliza (1) Read input (read list-of-words) (2) Find a pattern that matches the input (3) Transform the pattern to a response

57 Programming Eliza (1) Read input (read list-of-words) (2) Find a pattern that matches the input (3) Transform the pattern to a response (4) Print the response print

58

59

60

61 The original Eliza: Had more rules Alias method for associating several words with the same pattern (e.g. both mother and father with family Synonymy mechanism (e.g. don't = do not, everybody = everyone ) Separate response calculated for comma-separated sub phrases Set of outputs in case of no match (e.g. Tell me more about X, with X an earlier input) What is important is the technique of pattern matching and rul-based translation. => Next week: a more general pattern matching utility and STUDENT