SlideShare a Scribd company logo
ArtificiAl intelligence
15cS562
Ravi Kumar B N
Assistant Professor
Dept. of CSE
BMSIT&M
PROBLEMS,
PROBLEM SPACES
AND SEARCH
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
2
Contents
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
3
• Defining the problem as a State Space Search
• Production Systems
• Control Strategies
• Breadth First Search
• Depth First Search
• Heuristic Search
• Problem Characteristics
• Is the Problem Decomposable?
• Can Solution Steps be ignored or undone?
• Production system characteristics
• Issues in the design of search programs
To Build a System to Solve a Particular Problem,
The Following Four Things are Needed
1. Define the problem precisely- specify both initial
and final situations(state)
2. Analyze the problem
3. Isolate and represent the task knowledge that is
necessary to solve the problem
4. Choose the best problem solving technique and
apply it
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
4
State space search
Problem = Searching for a goal state
It is a process in which successive configurations or states of an
instance are considered , with the goal of finding a goal state with a
desired property
. State space- a set of states that a problem can be in.
- The group consisting of all the attainable states of a
problem
ex: Customers in a line would have state space {0,1,2….}
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
5
Search Problem
S: the full set of states
S0 :the initial state
A:SS set of operators
G : the set of final states.
G is subset of S
Search problem:
Find a sequence of actions which
transforms the agent from the
initial state to goal state.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
6
Representing search problems
Using directed graph
- The states are represented as nodes
- The allowed actions are represented as arcs.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
7
Problem Formulation
•A single state problem formulation is defined by four items
Initial state, successor function, goal test and path cost
•Problem formulation means choosing a relevant set of states
to consider, and a feasible set of operators for moving from
one state to another
•Search is the process of imagining sequences of operators
applied to the initial state and checking which sequence
reaches a goal state.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
8
Examples.
Problem: On holiday in Singapur; currently in Mysur. Flight
leaves tomorrow from Bangalore. Find a short route to drive
to Bangalore.
Formulate problem:
states: various cities
actions: drive between cities
solution: sequence of cities
Path Cost: distance travelled
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
9
Vacuum world state space
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
10
States: Dirt and Robot Location
Actions: Left, right, clean
Goal test: No dirt at all locations
Path cost: 1 per action
The 8 - Puzzle
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
11
The 8 - Puzzle
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
States: Locations of tiles
Actions: Move blank left, right, up, down
Goal test: Given
Path cost: 1 per move
12
State space search: Playing
Chess
• Each position can be described by an 8 by 8 array.
• Initial position is the game opening position.
• Goal position is any position in which the opponent does not
have a legal move and his or her king is under attack.
• Legal moves can be described by a set of rules:
-Left sides can be described by a set of rules
-Right sides describe the new resulting state
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
13
Playing chess contd…
• State space is a set of legal positions.
• Starting at the initial state.
• Using the set of rules to move from one state to another.
• Attempting to end up in a goal state.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
14
Playing Chess Contd..
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
15
One Legal Chess move
Playing Chess Contd..
• Writing the rules like above leads to very large number
• These rule poses serious practical difficulties
- No person could ever supply a complete set of rules. It
would take too long and could certainly not be done
without mistakes
- No program could easily handle all those rules.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
16
Playing Chess Contd..
Another way to describe the chess moves
White pawn at
Square(file e, rank 2) Move a pawn from
AND Square(file e, rank 2)
Square(file e, rank 3) is empty  to
AND Square(file e, rank 4)
Square(file e, rank 4) is empty
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
17
The Water Jug Problem
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
18
Given two jugs, a 4-gallon and 3-gallon, neither has any measuring maskers on it. There is a pump that
can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug?
1 Gallon = 3.785 Liter
The Water Jug Problem
The state space for this problem can be described as the set of
ordered pairs of integers (x,y) such that x = 0, 1,2, 3 or 4 and
y = 0,1,2 or 3; x represents the number of gallons of water in
the 4-gallon jug and y represents the quantity of water in 3-
gallon jug
The start state is (0,0)
The goal state is (2,n)
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
19
Production rules for Water Jug
Problem
The operators to be used to solve the problem can be described as
follows:
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
20
Production rules
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
21
To solve the water jug problem
•Required a control structure that loops through a simple
cycle in which some rule whose left side matches the current
state is chosen
• the appropriate change to the state is made as described in
the corresponding right side
•the resulting state is checked to see if it corresponds to goal
state.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
22
One solution to the water jug problem
Shortest such sequence will have a impact on the choice of appropriate
mechanism to guide the search for solution.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
23
Production Systems
To Structure AI Programs
A production system consists of:
•A set of rules, each consisting of a left side that determines the applicability of
the rule and a right side that describes the operation to be performed if that rule is
applied.
•One or more knowledge/databases that contain whatever information is
appropriate for the particular task. Some parts of the database may be permanent,
while other parts of it may pertain only to the solution of the current problem.
•A control strategy that specifies the order in which the rules will be compared
to the database and a way of resolving the conflicts that arise when several rules
match at once.
•A rule applier
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
24
Control Strategies
 How to decide which rule to apply next during the process
of searching for a solution to a problem?
 The two requirements of good control strategy are that
• It should cause motion.
• It should be systematic
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
25
BFS Tree for Water Jug
problem
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
26
(0,0)
(4,0) (0,3)
(4,3) (0,0) (1,3) (4,3) (0,0) (3,0)
Breadth First Search
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
27
Breadth First Search
Algorithm:
1. Create a variable called NODE-LIST and set it to initial
state
2. Until a goal state is found or NODE-LIST is empty do
a. Remove the first element from NODE-LIST and call it E. If NODE-
LIST was empty, quit
b. For each way that each rule can match the state described in E do:
i. Apply the rule to generate a new state
ii. If the new state is a goal state, quit and return this state
iii. Otherwise, add the new state to the end of NODE-LIST
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
28
Depth First Search
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
29
Depth First Search
Algorithm:
1.If the initial state is a goal state, quit and return success
2.Otherwise, do the following until success or failure is
signaled:
a. Generate a successor, E, of initial state. If there are no
more successors, signal failure.
b. Call Depth-First Search, with E as the initial state
c. If success is returned, signal success. Otherwise continue
in this loop.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
30
Backtracking
• In this search, we pursue a single branch of the tree until it
yields a solution or until a decision to terminate the path is
made.
• It makes sense to terminate a path if it reaches dead-end,
produces a previous state. In such a state backtracking occurs
• Chronological Backtracking: Order in which steps are undone
depends only on the temporal sequence in which steps were
initially made.
• Specifically most recent step is always the first to be undone.
• This is also simple backtracking.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
31
Advantages of Depth-First
Search
• DFS requires less memory since only the nodes on
the current path are stored.
• By chance, DFS may find a solution without
examining much of the search space at all
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
32
Advantages of BFS
• BFS will not get trapped exploring a blind alley.
• If there are multiple solutions, then a minimal
solution will be found.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
33
Problem Characteristics
Inorder to choose the most appropriate method for a particular
problem, it is necessary to analyze the problem along several
key dimensions:
• Is the problem decomposable into a set of independent smaller or
easier subproblems?
• Can solution steps be ignored or at least undone if they prove unwise?
• Is the problem’s universe predictable?
• Is a good solution to the problem obvious without comparison to all
other possible solutions?
• Is the desired solution a state of the world or a path to a state?
• Is a large amount of knowledge absolutely required to solve the
problem or is knowledge important only to constrain the search?
• Can a computer that is simply given the problem return the solution or
will the solution of the problem require interaction between the
computer and a person?
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
34
Is the problem
Decomposable?
• Whether the problem can be decomposed into
smaller problems?
• Using the technique of problem decomposition,
we can often solve very large problems easily.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
35
Symbolic Integration
Decomposable
Sigma(x2
+3x+sin2
xcos2
x)
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
36
Blocks World Problem
Non Decomposable
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
37
Following
operators are
available:
CLEAR(x) [ block x
has nothing on it]-
> ON(x, Table)
CLEAR(x) and
CLEAR(y) ->
ON(x,y) [ put x on
y]
C
A B
A
B
C
Start: ON(C,A)
Goal:
ON(B,C) and
ON(A,B)
ON(B,C)
ON(B,C) and ON(A,B)
ON(B,C)
ON(A,B)
CLEAR(A) ON(A,B)
CLEAR(A) ON(A,B)
Can Solution Steps be
ignored or undone?
Suppose we are trying to prove a math theorem. We can prove a lemma. If we find
the lemma is not of any help, we can still continue.
8-puzzle problem
Chess: A move cannot be taken back.
Important classes of problems:
• Ignorable ( theorem proving)
• Recoverable ( 8-puzzle)
• Irrecoverable ( Chess)
The recoverability of a problem plays an important role in determining the
complexity of the control structure necessary for the problem’s solution.
• Ignorable problems can be solved using a simple control structure that never
backtracks
• Recoverable problems can be solved by a slightly more complicated control
strategy that does sometimes make mistakes
• Irrecoverable problems will need to be solved by systems that expends a great
deal of effort making each decision since decision must be final.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
38
Is the universe Predictable?
• Certain Outcome ( ex: 8-puzzle)
• Uncertain Outcome ( ex: Bridge)
• For solving certain outcome problems, open loop approach
( without feedback) will work fine.
• For uncertain-outcome problems, planning can at best
generate a sequence of operators that has a good
probability of leading to a solution. We need to allow for a
process of plan revision to take place.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
39
Is a good solution absolute or
relative?
• Any path problem
• Best path problem
• Any path problems can often be solved in a reasonable
amount of time by using heuristics that suggest good
paths to explore.
• Best path problems are computationally harder.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
40
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
41
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
42
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
43
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
44
Is the solution a state or a
path?
Finding a consistent interpretation
For the sentence “The bank president ate a dish of pasta salad with
the fork”.
We need to find the interpretation but not the record of the
processing.
Water jug : Here it is not sufficient to report that we have
solved , but the path that we found to the state (2,0). Thus a
statement of a solution to this problem must be a sequence of
operations ( Plan) that produces the final state.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
45
Is the solution a state or a
path?
A path solution problem can be reformulated as a state –
solution problem by describing a state as a partial path to a
solution.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
46
What is the role of
knowledge?
Two examples:
• Playing Chess: Knowledge is required to constrain the
search for a solution
• Newspaper story understanding: Lot of knowledge is
required even to be able to recognize a solution.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
47
What is the role of
knowledge?
Consider a problem of scanning daily newspapers
“to decide which are supporting the democrats and which are
supporting the republicans in some upcoming election”.
We need lots of knowledge to answer such questions as:
• The names of the candidates in each party
• The facts that if the major thing you want to see done is have taxes lowered, you
are probably supporting the republicans
• The fact that if the major thing you want to see done is improved education for
minority students, you are probably supporting the democrats.
• etc
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
48
Does the task require Interaction
with a person?
The programs require intermediate interaction with people
for additional inputs and to provided reassurance to the user.
There are two types of problems:
• Solitary
• Conversational
Decision on using one of these approaches will be important
in the choice of problem solving method.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
49
Does the task require Interaction
with a person?
Solitary Problem: in which there is no intermediate
communication and no demand for an explanation of the
reasoning process.
Conversational Problem: In which intermediate
communication is to provide either additional assistance to
the computer or additional information to the user.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
50
Problem Classification
• There are several broad classes into which the problems
fall.
• These classes can each be associated with generic control
strategy that is appropriate for solving the problems:
• Most diagnostic task : ex: medical diagnostics, diagnosis of
faults in mechanical devices
• Propose and Refine: ex: design and planning
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
51
Production System
Characteristics
Production Systems are good way to describe the operations that
can be performed in a search for a solution to a problem.
1.Can production systems, like problems, be described by a set of
characteristics that shed some light on how they can easily be
implemented?
2.If so, what relationships are there between problem types and
the types of production systems best suited to solving the
problems?
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
52
Production System
Characteristics
To answer to the first question is yes. Consider the following
definitions of Classes of Production systems:
• Monotonic Production System
• Non-Monotonic Production system
• Partially commutative Production system:
• Commutative Production system- both monotonic and
partially commutative.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
53
Monotonic Production
Systems
Production system in which the application of a rule
never prevents the later application of another rule
that could also have been applied at the time the first
rule was applied.
i.e., rules are independent.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
54
Commutative Production
system
A partially Commutative production system has a property
that if the application of a particular sequence of rules
transform state x into state y, then any permutation of those
rules that is allowable, also transforms state x into state y.
A Commutative production system is a production system
that is both monotonic and partially commutative.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
55
Four Categories of Production
System
Monotonic NonMonotonic
Partially
Commutative
Theorem proving Robot Navigation
Not Partially
Commutative
Chemical
Synthesis
Bridge
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
56
Partially Commutative,
Monotonic
These production systems are useful for solving ignorable
problems.
Example: Theorem Proving
They can be implemented without the ability to backtrack to
previous states when it is discovered that an incorrect path
has been followed.
This often results in a considerable increase in efficiency,
particularly because since the database will never have to be
restored, It is not necessary to keep track of where in the
search process every change was made.
They are good for problems where things do not change; new
things get created.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
57
Non Monotonic, Partially
Commutative
• Useful for problems in which changes occur but can
be reversed and in which order of operations is not
critical.
• Example: Robot Navigation, 8-puzzle, blocks world
• Suppose the robot has the following ops: go North
(N), go East (E), go South (S), go West (W). To reach its
goal, it does not matter whether the robot executes the
N-N-E or N-E-N.
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
58
Not partially Commutative
Problems in which irreversible change occurs
Example: chemical synthesis
The ops can be :Add chemical x to the pot, Change the temperature
to t degrees.
These ops may cause irreversible changes to the potion being
brewed.
The order in which they are performed can be very important in
determining the final output.
(X+y) +z is not the same as (z+y) +x
Non partially commutative production systems are less likely to
produce the same node many times in search process.
When dealing with ones that describe irreversible processes, it is
partially important to make correct decisions the first time, although
if the universe is predictable, planning can be used to make that less
important.Ravi Kumar B N, Asst.Prof,CSE,BMSIT
59
Issues in the design of search
programs
• The direction in which to conduct the search
( forward versus backward reasoning).
• How to select applicable rules ( Matching)
• How to represent each node of the search process
( knowledge representation problem)
Ravi Kumar B N, Asst.Prof,CSE,BMSIT
60

More Related Content

What's hot

Np cooks theorem
Np cooks theoremNp cooks theorem
Np cooks theorem
Narayana Galla
 
Uninformed search /Blind search in AI
Uninformed search /Blind search in AIUninformed search /Blind search in AI
Uninformed search /Blind search in AI
Kirti Verma
 
5 csp
5 csp5 csp
5 csp
Mhd Sb
 
Heuristc Search Techniques
Heuristc Search TechniquesHeuristc Search Techniques
Heuristc Search Techniques
Jismy .K.Jose
 
2. forward chaining and backward chaining
2. forward chaining and backward chaining2. forward chaining and backward chaining
2. forward chaining and backward chaining
monircse2
 
State Space Representation and Search
State Space Representation and SearchState Space Representation and Search
State Space Representation and Search
Hitesh Mohapatra
 
Water jug problem ai part 6
Water jug problem ai part 6Water jug problem ai part 6
Water jug problem ai part 6
Kirti Verma
 
String matching algorithms
String matching algorithmsString matching algorithms
String matching algorithms
Ashikapokiya12345
 
Control Strategies in AI
Control Strategies in AIControl Strategies in AI
Control Strategies in AI
Amey Kerkar
 
Predicate logic
 Predicate logic Predicate logic
Predicate logic
Harini Balamurugan
 
Unification and Lifting
Unification and LiftingUnification and Lifting
Unification and Lifting
Megha Sharma
 
Propositional logic
Propositional logicPropositional logic
Propositional logic
Rushdi Shams
 
AI Lecture 3 (solving problems by searching)
AI Lecture 3 (solving problems by searching)AI Lecture 3 (solving problems by searching)
AI Lecture 3 (solving problems by searching)
Tajim Md. Niamat Ullah Akhund
 
Graph coloring using backtracking
Graph coloring using backtrackingGraph coloring using backtracking
Graph coloring using backtracking
shashidharPapishetty
 
State space search and Problem Solving techniques
State space search and Problem Solving techniquesState space search and Problem Solving techniques
State space search and Problem Solving techniques
Kirti Verma
 
BackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesBackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and Examples
Fahim Ferdous
 
Issues in knowledge representation
Issues in knowledge representationIssues in knowledge representation
Issues in knowledge representation
Sravanthi Emani
 
Dempster shafer theory
Dempster shafer theoryDempster shafer theory
Dempster shafer theory
Dr. C.V. Suresh Babu
 
A* Search Algorithm
A* Search AlgorithmA* Search Algorithm
A* Search Algorithm
vikas dhakane
 
Backtracking
Backtracking  Backtracking
Backtracking
Vikas Sharma
 

What's hot (20)

Np cooks theorem
Np cooks theoremNp cooks theorem
Np cooks theorem
 
Uninformed search /Blind search in AI
Uninformed search /Blind search in AIUninformed search /Blind search in AI
Uninformed search /Blind search in AI
 
5 csp
5 csp5 csp
5 csp
 
Heuristc Search Techniques
Heuristc Search TechniquesHeuristc Search Techniques
Heuristc Search Techniques
 
2. forward chaining and backward chaining
2. forward chaining and backward chaining2. forward chaining and backward chaining
2. forward chaining and backward chaining
 
State Space Representation and Search
State Space Representation and SearchState Space Representation and Search
State Space Representation and Search
 
Water jug problem ai part 6
Water jug problem ai part 6Water jug problem ai part 6
Water jug problem ai part 6
 
String matching algorithms
String matching algorithmsString matching algorithms
String matching algorithms
 
Control Strategies in AI
Control Strategies in AIControl Strategies in AI
Control Strategies in AI
 
Predicate logic
 Predicate logic Predicate logic
Predicate logic
 
Unification and Lifting
Unification and LiftingUnification and Lifting
Unification and Lifting
 
Propositional logic
Propositional logicPropositional logic
Propositional logic
 
AI Lecture 3 (solving problems by searching)
AI Lecture 3 (solving problems by searching)AI Lecture 3 (solving problems by searching)
AI Lecture 3 (solving problems by searching)
 
Graph coloring using backtracking
Graph coloring using backtrackingGraph coloring using backtracking
Graph coloring using backtracking
 
State space search and Problem Solving techniques
State space search and Problem Solving techniquesState space search and Problem Solving techniques
State space search and Problem Solving techniques
 
BackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesBackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and Examples
 
Issues in knowledge representation
Issues in knowledge representationIssues in knowledge representation
Issues in knowledge representation
 
Dempster shafer theory
Dempster shafer theoryDempster shafer theory
Dempster shafer theory
 
A* Search Algorithm
A* Search AlgorithmA* Search Algorithm
A* Search Algorithm
 
Backtracking
Backtracking  Backtracking
Backtracking
 

Similar to Problems, Problem spaces and Search

AI R16 - UNIT-2.pdf
AI R16 - UNIT-2.pdfAI R16 - UNIT-2.pdf
AI R16 - UNIT-2.pdf
JNTUK KAKINADA
 
Final slide (bsc csit) chapter 3
Final slide (bsc csit) chapter 3Final slide (bsc csit) chapter 3
Final slide (bsc csit) chapter 3
Subash Chandra Pakhrin
 
AI_Session 3 Problem Solving Agent and searching for solutions.pptx
AI_Session 3 Problem Solving Agent and searching for solutions.pptxAI_Session 3 Problem Solving Agent and searching for solutions.pptx
AI_Session 3 Problem Solving Agent and searching for solutions.pptx
Asst.prof M.Gokilavani
 
2.Problems Problem Spaces and Search.ppt
2.Problems Problem Spaces and Search.ppt2.Problems Problem Spaces and Search.ppt
2.Problems Problem Spaces and Search.ppt
Dr. Naushad Varish
 
AI-03 Problems State Space.pptx
AI-03 Problems State Space.pptxAI-03 Problems State Space.pptx
AI-03 Problems State Space.pptx
Pankaj Debbarma
 
Chapter 2 (final)
Chapter 2 (final)Chapter 2 (final)
Chapter 2 (final)
Nateshwar Kamlesh
 
Production system
Production systemProduction system
Production system
Amit Kumar Rathi
 
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptxAI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
Asst.prof M.Gokilavani
 
chapter 2 Problem Solving.pdf
chapter 2 Problem Solving.pdfchapter 2 Problem Solving.pdf
chapter 2 Problem Solving.pdf
MeghaGupta952452
 
CH4_AI_Lecture.ppt
CH4_AI_Lecture.pptCH4_AI_Lecture.ppt
CH4_AI_Lecture.ppt
AhmedNURHUSIEN
 
AI Lesson 03
AI Lesson 03AI Lesson 03
AI Lesson 03
Assistant Professor
 
Final-AI-Problem Solving.pdf
Final-AI-Problem Solving.pdfFinal-AI-Problem Solving.pdf
Final-AI-Problem Solving.pdf
harinathkuruva
 
Problems Spaces and Search
Problems Spaces and SearchProblems Spaces and Search
Problems Spaces and Search
ChaitanyaHanda
 
AI_Planning.pdf
AI_Planning.pdfAI_Planning.pdf
AI_Planning.pdf
SUSHMARATHI3
 
Chapter2final 130103081315-phpapp02
Chapter2final 130103081315-phpapp02Chapter2final 130103081315-phpapp02
Chapter2final 130103081315-phpapp02
Madhan Kumar
 
problemsolving with AI.pptx
problemsolving with AI.pptxproblemsolving with AI.pptx
problemsolving with AI.pptx
PriyadharshiniG41
 
Problem solving in Artificial Intelligence.pptx
Problem solving in Artificial Intelligence.pptxProblem solving in Artificial Intelligence.pptx
Problem solving in Artificial Intelligence.pptx
kitsenthilkumarcse
 
Dynamic Programming
Dynamic ProgrammingDynamic Programming
Dynamic Programming
contact2kazi
 
Amit ppt
Amit pptAmit ppt
Amit ppt
amitp26
 
study material for Artificial Intelligence
study material for Artificial Intelligencestudy material for Artificial Intelligence
study material for Artificial Intelligence
karmastrike9441
 

Similar to Problems, Problem spaces and Search (20)

AI R16 - UNIT-2.pdf
AI R16 - UNIT-2.pdfAI R16 - UNIT-2.pdf
AI R16 - UNIT-2.pdf
 
Final slide (bsc csit) chapter 3
Final slide (bsc csit) chapter 3Final slide (bsc csit) chapter 3
Final slide (bsc csit) chapter 3
 
AI_Session 3 Problem Solving Agent and searching for solutions.pptx
AI_Session 3 Problem Solving Agent and searching for solutions.pptxAI_Session 3 Problem Solving Agent and searching for solutions.pptx
AI_Session 3 Problem Solving Agent and searching for solutions.pptx
 
2.Problems Problem Spaces and Search.ppt
2.Problems Problem Spaces and Search.ppt2.Problems Problem Spaces and Search.ppt
2.Problems Problem Spaces and Search.ppt
 
AI-03 Problems State Space.pptx
AI-03 Problems State Space.pptxAI-03 Problems State Space.pptx
AI-03 Problems State Space.pptx
 
Chapter 2 (final)
Chapter 2 (final)Chapter 2 (final)
Chapter 2 (final)
 
Production system
Production systemProduction system
Production system
 
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptxAI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
AI3391 Artificial Intelligence Session 23 Backtracking CSP's.pptx
 
chapter 2 Problem Solving.pdf
chapter 2 Problem Solving.pdfchapter 2 Problem Solving.pdf
chapter 2 Problem Solving.pdf
 
CH4_AI_Lecture.ppt
CH4_AI_Lecture.pptCH4_AI_Lecture.ppt
CH4_AI_Lecture.ppt
 
AI Lesson 03
AI Lesson 03AI Lesson 03
AI Lesson 03
 
Final-AI-Problem Solving.pdf
Final-AI-Problem Solving.pdfFinal-AI-Problem Solving.pdf
Final-AI-Problem Solving.pdf
 
Problems Spaces and Search
Problems Spaces and SearchProblems Spaces and Search
Problems Spaces and Search
 
AI_Planning.pdf
AI_Planning.pdfAI_Planning.pdf
AI_Planning.pdf
 
Chapter2final 130103081315-phpapp02
Chapter2final 130103081315-phpapp02Chapter2final 130103081315-phpapp02
Chapter2final 130103081315-phpapp02
 
problemsolving with AI.pptx
problemsolving with AI.pptxproblemsolving with AI.pptx
problemsolving with AI.pptx
 
Problem solving in Artificial Intelligence.pptx
Problem solving in Artificial Intelligence.pptxProblem solving in Artificial Intelligence.pptx
Problem solving in Artificial Intelligence.pptx
 
Dynamic Programming
Dynamic ProgrammingDynamic Programming
Dynamic Programming
 
Amit ppt
Amit pptAmit ppt
Amit ppt
 
study material for Artificial Intelligence
study material for Artificial Intelligencestudy material for Artificial Intelligence
study material for Artificial Intelligence
 

More from BMS Institute of Technology and Management

Software Engineering and Introduction, Activities and ProcessModels
Software Engineering and Introduction, Activities and ProcessModels Software Engineering and Introduction, Activities and ProcessModels
Software Engineering and Introduction, Activities and ProcessModels
BMS Institute of Technology and Management
 
Python Regular Expressions
Python Regular ExpressionsPython Regular Expressions
Python Regular Expressions
BMS Institute of Technology and Management
 
Pytho_tuples
Pytho_tuplesPytho_tuples
Pytho dictionaries
Pytho dictionaries Pytho dictionaries
Pytho lists
Pytho listsPytho lists
File handling in Python
File handling in PythonFile handling in Python
Introduction to the Python
Introduction to the PythonIntroduction to the Python
Introduction to the Python
BMS Institute of Technology and Management
 
15CS562 AI VTU Question paper
15CS562 AI VTU Question paper15CS562 AI VTU Question paper
15CS562 AI VTU Question paper
BMS Institute of Technology and Management
 
weak slot and filler
weak slot and fillerweak slot and filler
strong slot and filler
strong slot and fillerstrong slot and filler
Introduction to Artificial Intelligence and few examples
Introduction to Artificial Intelligence and few examplesIntroduction to Artificial Intelligence and few examples
Introduction to Artificial Intelligence and few examples
BMS Institute of Technology and Management
 

More from BMS Institute of Technology and Management (11)

Software Engineering and Introduction, Activities and ProcessModels
Software Engineering and Introduction, Activities and ProcessModels Software Engineering and Introduction, Activities and ProcessModels
Software Engineering and Introduction, Activities and ProcessModels
 
Python Regular Expressions
Python Regular ExpressionsPython Regular Expressions
Python Regular Expressions
 
Pytho_tuples
Pytho_tuplesPytho_tuples
Pytho_tuples
 
Pytho dictionaries
Pytho dictionaries Pytho dictionaries
Pytho dictionaries
 
Pytho lists
Pytho listsPytho lists
Pytho lists
 
File handling in Python
File handling in PythonFile handling in Python
File handling in Python
 
Introduction to the Python
Introduction to the PythonIntroduction to the Python
Introduction to the Python
 
15CS562 AI VTU Question paper
15CS562 AI VTU Question paper15CS562 AI VTU Question paper
15CS562 AI VTU Question paper
 
weak slot and filler
weak slot and fillerweak slot and filler
weak slot and filler
 
strong slot and filler
strong slot and fillerstrong slot and filler
strong slot and filler
 
Introduction to Artificial Intelligence and few examples
Introduction to Artificial Intelligence and few examplesIntroduction to Artificial Intelligence and few examples
Introduction to Artificial Intelligence and few examples
 

Recently uploaded

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
Yasser Mahgoub
 
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELDEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
gerogepatton
 
CSM Cloud Service Management Presentarion
CSM Cloud Service Management PresentarionCSM Cloud Service Management Presentarion
CSM Cloud Service Management Presentarion
rpskprasana
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
KrishnaveniKrishnara1
 
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSA SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
IJNSA Journal
 
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
ML Based Model for NIDS MSc Updated Presentation.v2.pptxML Based Model for NIDS MSc Updated Presentation.v2.pptx
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
JamalHussainArman
 
Recycled Concrete Aggregate in Construction Part II
Recycled Concrete Aggregate in Construction Part IIRecycled Concrete Aggregate in Construction Part II
Recycled Concrete Aggregate in Construction Part II
Aditya Rajan Patra
 
spirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptxspirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptx
Madan Karki
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
MDSABBIROJJAMANPAYEL
 
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdfBPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
MIGUELANGEL966976
 
The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.
sachin chaurasia
 
Generative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of contentGenerative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of content
Hitesh Mohapatra
 
Textile Chemical Processing and Dyeing.pdf
Textile Chemical Processing and Dyeing.pdfTextile Chemical Processing and Dyeing.pdf
Textile Chemical Processing and Dyeing.pdf
NazakatAliKhoso2
 
Embedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoringEmbedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoring
IJECEIAES
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
171ticu
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
IJECEIAES
 
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
171ticu
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
bijceesjournal
 
Modelagem de um CSTR com reação endotermica.pdf
Modelagem de um CSTR com reação endotermica.pdfModelagem de um CSTR com reação endotermica.pdf
Modelagem de um CSTR com reação endotermica.pdf
camseq
 
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsKuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
Victor Morales
 

Recently uploaded (20)

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
 
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELDEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
 
CSM Cloud Service Management Presentarion
CSM Cloud Service Management PresentarionCSM Cloud Service Management Presentarion
CSM Cloud Service Management Presentarion
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
 
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSA SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
 
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
ML Based Model for NIDS MSc Updated Presentation.v2.pptxML Based Model for NIDS MSc Updated Presentation.v2.pptx
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
 
Recycled Concrete Aggregate in Construction Part II
Recycled Concrete Aggregate in Construction Part IIRecycled Concrete Aggregate in Construction Part II
Recycled Concrete Aggregate in Construction Part II
 
spirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptxspirit beverages ppt without graphics.pptx
spirit beverages ppt without graphics.pptx
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
 
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdfBPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
 
The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.The Python for beginners. This is an advance computer language.
The Python for beginners. This is an advance computer language.
 
Generative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of contentGenerative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of content
 
Textile Chemical Processing and Dyeing.pdf
Textile Chemical Processing and Dyeing.pdfTextile Chemical Processing and Dyeing.pdf
Textile Chemical Processing and Dyeing.pdf
 
Embedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoringEmbedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoring
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
 
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
 
Modelagem de um CSTR com reação endotermica.pdf
Modelagem de um CSTR com reação endotermica.pdfModelagem de um CSTR com reação endotermica.pdf
Modelagem de um CSTR com reação endotermica.pdf
 
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsKuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
 

Problems, Problem spaces and Search

  • 1. ArtificiAl intelligence 15cS562 Ravi Kumar B N Assistant Professor Dept. of CSE BMSIT&M
  • 2. PROBLEMS, PROBLEM SPACES AND SEARCH Ravi Kumar B N, Asst.Prof,CSE,BMSIT 2
  • 3. Contents Ravi Kumar B N, Asst.Prof,CSE,BMSIT 3 • Defining the problem as a State Space Search • Production Systems • Control Strategies • Breadth First Search • Depth First Search • Heuristic Search • Problem Characteristics • Is the Problem Decomposable? • Can Solution Steps be ignored or undone? • Production system characteristics • Issues in the design of search programs
  • 4. To Build a System to Solve a Particular Problem, The Following Four Things are Needed 1. Define the problem precisely- specify both initial and final situations(state) 2. Analyze the problem 3. Isolate and represent the task knowledge that is necessary to solve the problem 4. Choose the best problem solving technique and apply it Ravi Kumar B N, Asst.Prof,CSE,BMSIT 4
  • 5. State space search Problem = Searching for a goal state It is a process in which successive configurations or states of an instance are considered , with the goal of finding a goal state with a desired property . State space- a set of states that a problem can be in. - The group consisting of all the attainable states of a problem ex: Customers in a line would have state space {0,1,2….} Ravi Kumar B N, Asst.Prof,CSE,BMSIT 5
  • 6. Search Problem S: the full set of states S0 :the initial state A:SS set of operators G : the set of final states. G is subset of S Search problem: Find a sequence of actions which transforms the agent from the initial state to goal state. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 6
  • 7. Representing search problems Using directed graph - The states are represented as nodes - The allowed actions are represented as arcs. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 7
  • 8. Problem Formulation •A single state problem formulation is defined by four items Initial state, successor function, goal test and path cost •Problem formulation means choosing a relevant set of states to consider, and a feasible set of operators for moving from one state to another •Search is the process of imagining sequences of operators applied to the initial state and checking which sequence reaches a goal state. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 8
  • 9. Examples. Problem: On holiday in Singapur; currently in Mysur. Flight leaves tomorrow from Bangalore. Find a short route to drive to Bangalore. Formulate problem: states: various cities actions: drive between cities solution: sequence of cities Path Cost: distance travelled Ravi Kumar B N, Asst.Prof,CSE,BMSIT 9
  • 10. Vacuum world state space Ravi Kumar B N, Asst.Prof,CSE,BMSIT 10 States: Dirt and Robot Location Actions: Left, right, clean Goal test: No dirt at all locations Path cost: 1 per action
  • 11. The 8 - Puzzle Ravi Kumar B N, Asst.Prof,CSE,BMSIT 11
  • 12. The 8 - Puzzle Ravi Kumar B N, Asst.Prof,CSE,BMSIT States: Locations of tiles Actions: Move blank left, right, up, down Goal test: Given Path cost: 1 per move 12
  • 13. State space search: Playing Chess • Each position can be described by an 8 by 8 array. • Initial position is the game opening position. • Goal position is any position in which the opponent does not have a legal move and his or her king is under attack. • Legal moves can be described by a set of rules: -Left sides can be described by a set of rules -Right sides describe the new resulting state Ravi Kumar B N, Asst.Prof,CSE,BMSIT 13
  • 14. Playing chess contd… • State space is a set of legal positions. • Starting at the initial state. • Using the set of rules to move from one state to another. • Attempting to end up in a goal state. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 14
  • 15. Playing Chess Contd.. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 15 One Legal Chess move
  • 16. Playing Chess Contd.. • Writing the rules like above leads to very large number • These rule poses serious practical difficulties - No person could ever supply a complete set of rules. It would take too long and could certainly not be done without mistakes - No program could easily handle all those rules. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 16
  • 17. Playing Chess Contd.. Another way to describe the chess moves White pawn at Square(file e, rank 2) Move a pawn from AND Square(file e, rank 2) Square(file e, rank 3) is empty  to AND Square(file e, rank 4) Square(file e, rank 4) is empty Ravi Kumar B N, Asst.Prof,CSE,BMSIT 17
  • 18. The Water Jug Problem Ravi Kumar B N, Asst.Prof,CSE,BMSIT 18 Given two jugs, a 4-gallon and 3-gallon, neither has any measuring maskers on it. There is a pump that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug? 1 Gallon = 3.785 Liter
  • 19. The Water Jug Problem The state space for this problem can be described as the set of ordered pairs of integers (x,y) such that x = 0, 1,2, 3 or 4 and y = 0,1,2 or 3; x represents the number of gallons of water in the 4-gallon jug and y represents the quantity of water in 3- gallon jug The start state is (0,0) The goal state is (2,n) Ravi Kumar B N, Asst.Prof,CSE,BMSIT 19
  • 20. Production rules for Water Jug Problem The operators to be used to solve the problem can be described as follows: Ravi Kumar B N, Asst.Prof,CSE,BMSIT 20
  • 21. Production rules Ravi Kumar B N, Asst.Prof,CSE,BMSIT 21
  • 22. To solve the water jug problem •Required a control structure that loops through a simple cycle in which some rule whose left side matches the current state is chosen • the appropriate change to the state is made as described in the corresponding right side •the resulting state is checked to see if it corresponds to goal state. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 22
  • 23. One solution to the water jug problem Shortest such sequence will have a impact on the choice of appropriate mechanism to guide the search for solution. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 23
  • 24. Production Systems To Structure AI Programs A production system consists of: •A set of rules, each consisting of a left side that determines the applicability of the rule and a right side that describes the operation to be performed if that rule is applied. •One or more knowledge/databases that contain whatever information is appropriate for the particular task. Some parts of the database may be permanent, while other parts of it may pertain only to the solution of the current problem. •A control strategy that specifies the order in which the rules will be compared to the database and a way of resolving the conflicts that arise when several rules match at once. •A rule applier Ravi Kumar B N, Asst.Prof,CSE,BMSIT 24
  • 25. Control Strategies  How to decide which rule to apply next during the process of searching for a solution to a problem?  The two requirements of good control strategy are that • It should cause motion. • It should be systematic Ravi Kumar B N, Asst.Prof,CSE,BMSIT 25
  • 26. BFS Tree for Water Jug problem Ravi Kumar B N, Asst.Prof,CSE,BMSIT 26 (0,0) (4,0) (0,3) (4,3) (0,0) (1,3) (4,3) (0,0) (3,0)
  • 27. Breadth First Search Ravi Kumar B N, Asst.Prof,CSE,BMSIT 27
  • 28. Breadth First Search Algorithm: 1. Create a variable called NODE-LIST and set it to initial state 2. Until a goal state is found or NODE-LIST is empty do a. Remove the first element from NODE-LIST and call it E. If NODE- LIST was empty, quit b. For each way that each rule can match the state described in E do: i. Apply the rule to generate a new state ii. If the new state is a goal state, quit and return this state iii. Otherwise, add the new state to the end of NODE-LIST Ravi Kumar B N, Asst.Prof,CSE,BMSIT 28
  • 29. Depth First Search Ravi Kumar B N, Asst.Prof,CSE,BMSIT 29
  • 30. Depth First Search Algorithm: 1.If the initial state is a goal state, quit and return success 2.Otherwise, do the following until success or failure is signaled: a. Generate a successor, E, of initial state. If there are no more successors, signal failure. b. Call Depth-First Search, with E as the initial state c. If success is returned, signal success. Otherwise continue in this loop. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 30
  • 31. Backtracking • In this search, we pursue a single branch of the tree until it yields a solution or until a decision to terminate the path is made. • It makes sense to terminate a path if it reaches dead-end, produces a previous state. In such a state backtracking occurs • Chronological Backtracking: Order in which steps are undone depends only on the temporal sequence in which steps were initially made. • Specifically most recent step is always the first to be undone. • This is also simple backtracking. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 31
  • 32. Advantages of Depth-First Search • DFS requires less memory since only the nodes on the current path are stored. • By chance, DFS may find a solution without examining much of the search space at all Ravi Kumar B N, Asst.Prof,CSE,BMSIT 32
  • 33. Advantages of BFS • BFS will not get trapped exploring a blind alley. • If there are multiple solutions, then a minimal solution will be found. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 33
  • 34. Problem Characteristics Inorder to choose the most appropriate method for a particular problem, it is necessary to analyze the problem along several key dimensions: • Is the problem decomposable into a set of independent smaller or easier subproblems? • Can solution steps be ignored or at least undone if they prove unwise? • Is the problem’s universe predictable? • Is a good solution to the problem obvious without comparison to all other possible solutions? • Is the desired solution a state of the world or a path to a state? • Is a large amount of knowledge absolutely required to solve the problem or is knowledge important only to constrain the search? • Can a computer that is simply given the problem return the solution or will the solution of the problem require interaction between the computer and a person? Ravi Kumar B N, Asst.Prof,CSE,BMSIT 34
  • 35. Is the problem Decomposable? • Whether the problem can be decomposed into smaller problems? • Using the technique of problem decomposition, we can often solve very large problems easily. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 35
  • 37. Blocks World Problem Non Decomposable Ravi Kumar B N, Asst.Prof,CSE,BMSIT 37 Following operators are available: CLEAR(x) [ block x has nothing on it]- > ON(x, Table) CLEAR(x) and CLEAR(y) -> ON(x,y) [ put x on y] C A B A B C Start: ON(C,A) Goal: ON(B,C) and ON(A,B) ON(B,C) ON(B,C) and ON(A,B) ON(B,C) ON(A,B) CLEAR(A) ON(A,B) CLEAR(A) ON(A,B)
  • 38. Can Solution Steps be ignored or undone? Suppose we are trying to prove a math theorem. We can prove a lemma. If we find the lemma is not of any help, we can still continue. 8-puzzle problem Chess: A move cannot be taken back. Important classes of problems: • Ignorable ( theorem proving) • Recoverable ( 8-puzzle) • Irrecoverable ( Chess) The recoverability of a problem plays an important role in determining the complexity of the control structure necessary for the problem’s solution. • Ignorable problems can be solved using a simple control structure that never backtracks • Recoverable problems can be solved by a slightly more complicated control strategy that does sometimes make mistakes • Irrecoverable problems will need to be solved by systems that expends a great deal of effort making each decision since decision must be final. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 38
  • 39. Is the universe Predictable? • Certain Outcome ( ex: 8-puzzle) • Uncertain Outcome ( ex: Bridge) • For solving certain outcome problems, open loop approach ( without feedback) will work fine. • For uncertain-outcome problems, planning can at best generate a sequence of operators that has a good probability of leading to a solution. We need to allow for a process of plan revision to take place. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 39
  • 40. Is a good solution absolute or relative? • Any path problem • Best path problem • Any path problems can often be solved in a reasonable amount of time by using heuristics that suggest good paths to explore. • Best path problems are computationally harder. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 40
  • 41. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 41
  • 42. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 42
  • 43. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 43
  • 44. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 44
  • 45. Is the solution a state or a path? Finding a consistent interpretation For the sentence “The bank president ate a dish of pasta salad with the fork”. We need to find the interpretation but not the record of the processing. Water jug : Here it is not sufficient to report that we have solved , but the path that we found to the state (2,0). Thus a statement of a solution to this problem must be a sequence of operations ( Plan) that produces the final state. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 45
  • 46. Is the solution a state or a path? A path solution problem can be reformulated as a state – solution problem by describing a state as a partial path to a solution. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 46
  • 47. What is the role of knowledge? Two examples: • Playing Chess: Knowledge is required to constrain the search for a solution • Newspaper story understanding: Lot of knowledge is required even to be able to recognize a solution. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 47
  • 48. What is the role of knowledge? Consider a problem of scanning daily newspapers “to decide which are supporting the democrats and which are supporting the republicans in some upcoming election”. We need lots of knowledge to answer such questions as: • The names of the candidates in each party • The facts that if the major thing you want to see done is have taxes lowered, you are probably supporting the republicans • The fact that if the major thing you want to see done is improved education for minority students, you are probably supporting the democrats. • etc Ravi Kumar B N, Asst.Prof,CSE,BMSIT 48
  • 49. Does the task require Interaction with a person? The programs require intermediate interaction with people for additional inputs and to provided reassurance to the user. There are two types of problems: • Solitary • Conversational Decision on using one of these approaches will be important in the choice of problem solving method. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 49
  • 50. Does the task require Interaction with a person? Solitary Problem: in which there is no intermediate communication and no demand for an explanation of the reasoning process. Conversational Problem: In which intermediate communication is to provide either additional assistance to the computer or additional information to the user. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 50
  • 51. Problem Classification • There are several broad classes into which the problems fall. • These classes can each be associated with generic control strategy that is appropriate for solving the problems: • Most diagnostic task : ex: medical diagnostics, diagnosis of faults in mechanical devices • Propose and Refine: ex: design and planning Ravi Kumar B N, Asst.Prof,CSE,BMSIT 51
  • 52. Production System Characteristics Production Systems are good way to describe the operations that can be performed in a search for a solution to a problem. 1.Can production systems, like problems, be described by a set of characteristics that shed some light on how they can easily be implemented? 2.If so, what relationships are there between problem types and the types of production systems best suited to solving the problems? Ravi Kumar B N, Asst.Prof,CSE,BMSIT 52
  • 53. Production System Characteristics To answer to the first question is yes. Consider the following definitions of Classes of Production systems: • Monotonic Production System • Non-Monotonic Production system • Partially commutative Production system: • Commutative Production system- both monotonic and partially commutative. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 53
  • 54. Monotonic Production Systems Production system in which the application of a rule never prevents the later application of another rule that could also have been applied at the time the first rule was applied. i.e., rules are independent. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 54
  • 55. Commutative Production system A partially Commutative production system has a property that if the application of a particular sequence of rules transform state x into state y, then any permutation of those rules that is allowable, also transforms state x into state y. A Commutative production system is a production system that is both monotonic and partially commutative. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 55
  • 56. Four Categories of Production System Monotonic NonMonotonic Partially Commutative Theorem proving Robot Navigation Not Partially Commutative Chemical Synthesis Bridge Ravi Kumar B N, Asst.Prof,CSE,BMSIT 56
  • 57. Partially Commutative, Monotonic These production systems are useful for solving ignorable problems. Example: Theorem Proving They can be implemented without the ability to backtrack to previous states when it is discovered that an incorrect path has been followed. This often results in a considerable increase in efficiency, particularly because since the database will never have to be restored, It is not necessary to keep track of where in the search process every change was made. They are good for problems where things do not change; new things get created. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 57
  • 58. Non Monotonic, Partially Commutative • Useful for problems in which changes occur but can be reversed and in which order of operations is not critical. • Example: Robot Navigation, 8-puzzle, blocks world • Suppose the robot has the following ops: go North (N), go East (E), go South (S), go West (W). To reach its goal, it does not matter whether the robot executes the N-N-E or N-E-N. Ravi Kumar B N, Asst.Prof,CSE,BMSIT 58
  • 59. Not partially Commutative Problems in which irreversible change occurs Example: chemical synthesis The ops can be :Add chemical x to the pot, Change the temperature to t degrees. These ops may cause irreversible changes to the potion being brewed. The order in which they are performed can be very important in determining the final output. (X+y) +z is not the same as (z+y) +x Non partially commutative production systems are less likely to produce the same node many times in search process. When dealing with ones that describe irreversible processes, it is partially important to make correct decisions the first time, although if the universe is predictable, planning can be used to make that less important.Ravi Kumar B N, Asst.Prof,CSE,BMSIT 59
  • 60. Issues in the design of search programs • The direction in which to conduct the search ( forward versus backward reasoning). • How to select applicable rules ( Matching) • How to represent each node of the search process ( knowledge representation problem) Ravi Kumar B N, Asst.Prof,CSE,BMSIT 60