Problem Representation in Ai:

1. DEFINE THE PROBLEM PRECISELY :LIKE WHAT IS INITIAL SITUATION, WHAT WILL BE THE FINAL, ACCEPTABLE SOLUTIONS.

2. ANALYZE THE PROBLEM: VARIOUS POSSIBLE TECHNIQUES FOR SOLVING 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

PROBLEM REPRESENTATION IN AI:

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Biomedical Department, NIT Raipur

Methods of problem representation in AI

State space representation

“A set of all possible states for a given problem is known as the state space of the problem.”

or “A state space represents a problem in terms

of states and operators that change states.”

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Biomedical Department, NIT Raipur

A problem space consists of :

Precondition/An initial state

Post condition/Final states ( Goal State)

Actions

Total Cost

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Biomedical Department, NIT Raipur

EXAMPLE OF PROBLEM SPACE

If one wants to make a cup of coffee.What one have to do:

analyze the problem

check necessary ingredients are available or not.

if they are available ,apply procedure of making coffee ( Actions).

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Biomedical Department, NIT Raipur

STATE SPACE REPRESENTATION OF COFFEE MAKING

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Biomedical Department, NIT Raipur

What have we done?

1. We started with Ingredients i.e the Initial state.

2. Followed by sequence of Steps.3. We added only needed amount of coffee

powder, milk & sugar. These are Operators/ Actions.

4. At last had a cup of coffee –Goal state.

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Biomedical Department, NIT Raipur

ANOTHER EXAMPLE: WATER JUG PROBLEM

PROBLEM Given: 1.Two Jugs: one 4 gallon & one 3 gallon.2. No measuring markers.3. There is a pump that can be used to fill jug

with waters.4. How can you get exactly 2 gallons of water

in to 4-gallon jug?

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Biomedical Department, NIT Raipur

PROBLEM SPACE

Initial States– amount of water in both jugs.

Actions—Empty large/small, pour from large/small

Goal—specified amount of water in both jugPath cost—total no of actions applied

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Biomedical Department, NIT Raipur

Another Example: Find a driving route from city A to

city B

Problem Space:1.States– location specified by city .

2.Actions– driving along the roads between cities

3.Goal— city B4.Path cost—total distance or expected travel

time.

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Biomedical Department, NIT Raipur

STATE APACE FOR WATER JUG PROBLEM

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State: (x,y) x= 0,1,2,3, or 4 and, y= 0,1,2, or 3 x represents the number of gallons of water in

4-gallon jug y represents the number of gallons of water in

3-gallon jug Start state: (0,0); Goal state: (2,n); n is not specified in question. Operators: Various operations/actions which can

be carried out. Path Cost: Total no of steps.

ANOTHER EXAMPLE

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Example: Consider a 4-puzzle problem, where in a 4-cell board there are 3 cells filled with digits and 1 blank cell. The initial state of the game represents a particular orientation of the digits in the cells and the final state to be achieved is another orientation supplied to the game player. The problem of the game is to reach from the given initial state to the goal (final) state, if possible, with a minimum of moves. Let the initial and the final state be as shown in figures 1(a) and (b) respectively.

Operators: 1.blank-up (BU) 2.blank-down (BD) 3. blank-left (BL) 4. blank-right (BR)

STATE SPACE TREE FOR 4 PUZZLE PROBLEM

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