1. Problem Representation

2. CONTENTS State space Representation Problem Reduction
Definition Of Problem Representation
Methods of problem representation in AI
State space Representation
Advantages of State Space Representation
Disadvantages of State Space Representation
Problem Reduction

3. Definition Of Problem Representation
Before a solution can be found, the prime condition is that the problem must be very precisely defined.
By defining it properly, one convert the abstract problem into real workable states that are really understood.
These states are operated upon by a set of operators and the decision of which operator to be applied, when and where is dictated by the overall control strategy.
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4. Methods of Problem Representation in AI
State Space Representation
Problem Reduction
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5. State space Representation

6. Fig-State Space Representation For Coffee Making
To Define a Problem as a state space search, We will take the following example:
Water
Boiled
Boiling Water
Added Coffee Powder
Added Milk Powder
Decoction
Milk
Coffee
Added Sugar
Palatable Coffee
Fig-State Space Representation For Coffee Making

7. 1 5 3 1 2 3 6 8 7 4 5 6 4 2 7 8 Initial State Goal State
Thus, A set of all possible states for a given problem is known as the state space of the problem.
To explain it in a more detailed manner let us consider another problem of 8-puzzle.
The puzzle consists of a square frame containing 8 tiles and an empty slot. The tiles are numbered from 1 to 8.
The goal is to get the square in a numerical order. To solve this problem, one needs to have an initial state, a goal state & a set of rules.
Following figure shows the initial state and goal state. 1 5 3 1 2 3 6 8 7 4 5 6 4 2 7 8
Initial State
Goal State

8. The rules for this problem are:
The state space is now a directed graph with all the states as nodes. A node is said to exist if it is possible to obtain it from the initial state by application of a set of operators.
Up:-
If the hole is not touching the top frame, move it up.
Down:-
If the hole is not touching the bottom frame, move it down.
Left:-
If the hole is not touching the left frame, move it down.
Right:-
If the hole is not touching the right frame, move it down.

9. (Fragment of the state space of 8-tile puzzle)
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10. Advantages of State Space Representation
State space representation is highly beneficial in AI because they provide all possible states, operations and the goals.
If the entire state space representation for problem is given,it is possible to trace the path from the initial state to the goal state & identify the sequence of operators necessary for doing it.
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11. Disadvantages of State Space Representation
The major deficiency of this method is that it is not possible to visualize all states for a given problem.
The resources of the computer system are limited to handle huge state space representation.
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12. Problem Reduction
To overcome the deficiencies of above method, problem reduction technique comes today.
In this method, a complex problem is broken down or decomposed into a set of primitive sub-problems. solutions for this primitive sub-problem are easily obtained.
For Exp:-
Consider the activities that must be done to set right a punctured tyre.

13. Set right a punctured tyre
AND tree
Take the tyre to Mechanic
Identify the location of puncture
Fix the puncture
Remove the tyre
OR tree
Let the mechanic come and take it
You yourself remove it
Ask your friend to do it
Ask the mechanic
to do it
You yourself take it
Drive in your friend’s vehicle
Take it in a public transportation system
Fig-An AND/OR tree

14. The top level specifies the overall goal which is combination of tasks given in level2,level3 & level4 indicate primitive sub-problems.
The figure given in previous slide is a pictorial representation of problem by an AND/OR tree.
An arc( ) connecting different branches is called an AND tree.
Normally, the initial complex problem forms the parent node & primitive sub-problems form the leaf node.
Between the complex problem and the sub-problem, there exist two kinds of relationships -AND relationship and OR relationship.

15. In AND relationship, the solution for the problem is obtained by solving all the sub-problems.
In OR relationship, the solution for the problem is obtained by solving any of the sub-problems.
Most problem that AI attack, do not reduce to pure AND or pure OR trees. A combination of these exist.
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16. THANKS
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