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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State Space Representation

Problem Reduction

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State space Representation

To Define a Problem as a state space search, We will take the following example:

Water

Boiling Water

Decoction

Milk

Coffee

Palatable Coffee

Added Milk Powder

Added Sugar

Added Coffee Powder

Boiled

Fig-State Space Representation For Coffee Making

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.

87

654

3211 5

8

3

6 7

4 2

Initial State Goal State

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.

(Fragment of the state space of 8-tile puzzle)

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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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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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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.

Set right a punctured tyre

Remove the tyre

Take the tyre to Mechanic

Identify the location of puncture

Fix the puncture

You yourself remove it

Ask your friend to do it

Ask the mechanic to do it

You yourself take it

Let the mechanic come and take it

Drive in your friend’s vehicle

Take it in a public transportation system

AND tree

OR tree

Fig-An AND/OR tree

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.

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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