Lecture-2-AI-Problems- Problem space

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					Introduction to
Artificial Intelligence

          Dr. Osama fathy
Problems, Problem space
and Search
Some AI task Domains
Mundane tasks:
 Natural language: generation, understanding,
 translation,…
 Perception: vision, smelling, hearing, ……
 Robot control
 Commonsense reasoning: is a reasoning about
 physical object and their relation ships to each
 other , reasoning about actions and reaction

                                                    3
Some AI task Domains
Formal tasks:
  Math : logic, geometry, integral calculus,….. ,
  Games : chess, checkers, backgammon, ……..
  Expert tasks:
    Engineering: design, fault finding
    manufacturing planning
    Analysis: Scientific, Military, Medical,
    Financial …….

                                                    4
AI What AI can do?
Intelligence systems can help experts to solve
difficult analysis problems (military, financial, ..)
Intelligence systems can help to design new
devices (car's, airplane, ……….)
Intelligence systems can learn from examples
(artificial neural networks , expert sys's)
Intelligence systems can provide answer to
English questions using both structured data and
free text (Asimo. politic, ……)
                                                        5
 Script problem

Draw a script (is a structure that represents the
system's knowledge about a subject) of
shopping text. Then, write an algorithm to
solve the questions.




                                                    6
Script problem
  Mary went to store.
  Mary went shopping for a new coat.
  Mary walked up to sales person.
  She asked her if she needed any help.
  She asked where the coat department.
  She found a red one she really liked.
  When she got it home, she discovered that it went
  perfectly with here favorite dress

                                                  7
 Script problem
Q1: What did Mary go shopping for?
Q2: What did Mary find that she liked?
Q3: Did Mary buy any thing?




                                         8
Solution

1. Arrange actions Time.
2. Coding:
           C……...customer
           S………store
           P………sales person
           M….......merchandize
           D………money
           R………color
           T…….…department

                                  9
                                                                  1- C enter S



              3. Script:                                      2- C looking around



                                           3- C looks for a specific M       4- C looks for interesting M



                                                5- C ask P for help



                                                        6-



                 7- C find M                                                           8- C fails to find M



 9- C buy m                    10- C leaves s                         11- C leaves s                        12- C go to step 2



13- C takes M



14- C leaves S

                                                                                                                           10
4. Algorithms:




                 11
  Assignment-2:
  Prepare two different texts about two different
  subjects, and three questions about each one then:
  ►Draw a script for each one
  ► Write an algorithm to solve the questions
     for each one


Note: Last date to receipt (hard & soft copy the assignments,
next --------------


                                                                12
Problem representation
 State space representation:
   States.
   Operators.
   Initial and goal states.
 Problem reduction representation:
   Initial problem description.
   Set of operators for transforming problems to sub
   problems.
   Set of primitive problem description.
 Game tree.
                                                       13
A-State space representation:
 Define the state space that contain all the possible
 configurations of the relevant objects.
 Specify one or more states within that space from
 which the problem solving process will start
 (initial states).
 Specify one or more states that would be
 acceptable as solution to the problem (goal state).
 Specify a set of rules that describe the actions
 (operators) available.


                                                        14
Example: Water Jug Problem:
You are given to jugs 4-gallon one and 3-gallon
one, neither has measuring markers on it. There
is a pump that can be used to fill the jugs with
water. How can you get exactly 2-gallon of
water into the 4-gallon jug?




                    4-G        3-G

                                                   15
In order to solve the problem:
    Define the problem state space including the
    start and the goal states and a set of operators
    for moving in that space.
    The problem can then be solved by searching
    for a path through the space from the initial
    state to the goal state, So the process of search
    is fundamental to the problem solving process.
    Examples of basic search techniques:
        Breadth-first search.
        Depth-first search.
                                                        16
Example: Water Jug Problem
Solution:
 State Space: order pairs of integers (x, y) such
 that x = 0, 1, 2, 3, 4 and y = 0, 1, 2, 3.
 Start state: is (0, 0).
 Goal state: is (2, n) for any value of n.




                                                    17
Example: Water Jug Problem
 Operators:
  # Current     New       Condition    Description
     State      State
  1   (x, y)    (4, y)       x<4       Fill 4-G jug
  2   (x, y)    (x, 3)      y<3        Fill 3-G jug
  3   (x, y)   (x-d, y)     x>0       Pour some water
                                      from the 4-G jug
  4   (x, y)   (x, y-d)     y>0       Pour some water
                                      from the 3-G jug


                                                         18
Example: Water Jug Problem


  # Current      New         Condition     Description
     State       State
  5   (x, y)     (0, y)         x>0      Empty the 4-G jug
                                          on the ground
  6   (x, y)     (x, 0)        y>0       Empty the 3-G jug
                                          on the ground
  7   (x, y)   (4,y-(4-x))   x+y≥4 &      pour water from
                               y>0        3-G jug into 4-G
                                          jug until it is full
                                                                 19
Example: Water Jug Problem
  # Current       New         Condition     Description
     State        State
  8    (x, y)   (x-(3-y),3)   x+y≥3 &      pour water from
                                x>0        4-G jug into 3-G
                                           jug until it is full
  9    (x, y)    (x+y,0)      x+y≤4 &     pour all the water
                                y>0       from 3-G jug into
                                               4-G jug
  10   (x, y)    (0, x+y)     x+y≤3 &     pour all the water
                                x>0       from 4-G jug into
                                               3-G jug
                                                                  20
Example: Water Jug Problem
 Tree:          (0,0)

             (4,0)                              (0,3)


   (4,3)     (0,0)      (1,3)           (4,3)   (0,0)   (3,0)



     (0,3)     (1,0)      (4,0)     (4,3)


                (2,0)           (2,3)                           21
Example: travel salesman problem
A sales man has a list of cites, each of which he
must visit once. There are direct roads between
each pair of cites. Find the route the salesman
should follow for the shortest possible round
trip.
                          S,G




                                                    22
Example: travel salesman problem
State space for the problem:
     A simple control structure solve the problem so
     it will simply explore all paths in the tree and
     return the shortest one.
     If there are N cites, the number of different
     paths among them is (N-1)!
     if N= 10 cites, then different paths = 9!=362880
     So, the time required to perform this search is
     proportional to N!
     if N= 10 cites, then time = 10!=3628800 which
     is very large
                                                    23
    Example: travel salesman problem
                             A

        AB                   AC                      AD


 ABC         ABD      ACB         ACD         ADB         ADC


 ABCD        ABDC     ACBD        ACDB        ADBC        ADCB



                                          A                      B



N= 4 cites, then different paths = 3!=6
                                                D           C
                                                                     24
Problem representation
 State space representation:
   States.
   Operators.
   Initial and goal states.
 Problem reduction representation:
   Initial problem description.
   Set of operators for transforming problems to sub
   problems.
   Set of primitive problem description.
 Game tree.
                                                       25
B- Problem reduction representation
In this approach the initial problem description is
given and it is solved by a sequence of
transformations (operators) that changes it into a set
of sub-problems whose solutions are immediate
(primitive problems).
Problem representation:
   Initial problem description.
   A set of operators for transforming problem to
   sub-problems.
   A set of primitive problem descriptions.          26
       Example: Tower of Hanoi puzzle

   A                                                       A
   B                                                       B
   C                                                       C

           1            2   3        1       2       3
        initial state                            final state

There are three pegs, 1, 2 and 3, and three disks, a, b and c
(a being the smallest and c being the biggest). Initially, all
the disks are stacked on peg 1. The problem is to transfer
them all on to peg 3. Only one disk can be moved at a time,
and no disk can ever be placed on top of a smaller disk.
                                                                 27
Example: Tower of Hanoi puzzle
 The problem of moving a stack of size N from peg
 (1) to peg (3) can replaced by three problems:
  Moving a stack of size (n-1) from (1)     (2).
  Moving a stack of size (1) from (1)       (3).
  Moving a stack of size (n-1) from (2)     (3).
 Primitive problem:
 Moving a single disk from one peg to another
 provided no smaller disk is on the receiving peg.


                                                28
Solution:




            29
Example: Measuring problem!


                          9l
           3l      5l




Problem: Using these three buckets,
          measure 7 liters of water.

                                       30
    Example: Measuring problem!
(one possible) Solution:

      a        b           c                     9l
      0        0           0   start
                                       3l   5l
      3        0           0
      0        0           3
                                       a     b   c
      3        0           3
      0        0           6
      3        0           6
      0        3           6
      3        3           6
      1        5           6
      0        5           7   goal




                                                      31
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          32

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          33

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          34

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          35

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          36

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          37

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          38

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          39

  0    3    6
  Example: Measuring problem!
(one possible)
Solution:                         9l
                        3l   5l

  a    b    c           a     b   c

  0    0    0   start
  3    0    0
  0    0    3
  3    0    3
  0    0    6
  3    0    6                          40

  0    3    6
  Example: Measuring problem!
Another Solution:
                                9l
                      3l   5l
  a   b   c
  0   0   0   start   a     b   c

  0   5   0
  0   0   3
  3   0   3
  0   0   6
  3   0   6
  0   3   6                          41

  3   3   6
  Example: Measuring problem!
Another Solution:
                                9l
                      3l   5l
  a   b   c
  0   0   0   start   a     b   c

  0   5   0
  3   2   0
  0   0   3
  3   0   3
  0   0   6
  3   0   6
                                     42
  0   3   6
   Example: Measuring problem!
Another Solution:

                                           9l
    a      b        c
                                 3l   5l
    0      0        0   start
    0      5        0
                                 a     b   c
    3      2        0
    3      0        2
    3      0        3
    0      0        6
    3      0        6
    0      3        6
    3      3        6
    1      5        6
    0      5        7   goal
                                                43
  Example: Measuring problem!
Another Solution:
                                9l
                      3l   5l
  a   b   c
  0   0   0   start   a     b   c

  0   5   0
  3   2   0
  3   0   2
  3   5   2
  0   0   6
  3   0   6
                                     44
  0   3   6
  Example: Measuring problem!
Another Solution:
                                9l
                      3l   5l
  a   b   c
  0   0   0   start   a     b   c

  0   5   0
  3   2   0
  3   0   2
  3   5   2
  3   0   7   goal
  3   0   6
                                     45
  0   3   6
          Which solution• do we prefer?
• Solution 1:             Solution 2:

      a         b   c           a   b   c
      0         0   0   start   0   0   0   start
      3         0   0           0   5   0
      0         0   3           3   2   0
      3         0   3           3   0   2
      0         0   6           3   5   2
      3         0   6           3   0   7   goal
      0         3   6
      3         3   6
      1         5   6
      0         5   7   goal


                                              46

				
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