1. Introduction
Defining the Problem as a State Space Search

2. Defining the Problem as a State Space Search
The state space search representation forms the basis of most of the AI method. Its structure corresponds to the structure problem solving in two important ways:
If allows for a formal definition of a problem as the need to convert some given situation into some desired situation using a set of permissible operation.
It permits us to define the process of solving a particular problem as a combination of known techniques and search. The general technique of exploring the space to try to find some path from the current state to a good state.

3. Defining the Problem as a State Space Search(cont..)
Search is very important process in the solution of hard problem for which no more direct technique are available.
In order to provide a formal description of a problem it is necessary to do the following things:
 Define a state space that contains all the possible configurations of the relevant objects.
Specify one or more states within that space that describe possible situation from which the problem solving process may start. These states are called the initial states.
Specify one or more states that would be acceptable as solution to the problem. These states are called goal states.
Specify a set of rules that describe the actions (operators) available.

4. Water Jug Problem:
Problem: You are given two jugs. A 4 gallon one and a 3 gallon one. Neither has any measuring marker 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?
Solution: The state space for this problem can be described as a set of ordered pair of integers (x, y) such that x = 0, 1, 2, 3, 4 and y = 0, 1, 2, 3. x represent the numbers of gallon of water in 4 gallon jug and y represent the numbers of gallon of water in 3 gallon jug. The start state is (0, 0). The goal state is (2, n) for any value of n because the problem does not specify how many gallon need to be in the 3 gallon jug.

5. Production Rules of WJ Problem

6. Assumptions
 We have assumed that we can fill a jug from the pump and we can pour water out of a jug onto the ground. There are no measuring device:
Sample Solution:

7. Production Systems
Production system provide the structure for solving the AI problem. It consist of :
 A set of rules each consisting of a left side determines the applicability and right side that describes the operation to be performed.
One or more knowledge/ database that convert whatever information is appropriate for the particular task.
A control strategy that specify 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

8. Control Strategies
Control Strategy deal with how to decide which rule to apply next during the process of searching for a solution to a problem because it may happen more than one rule will have its left side match the current state.
 The first requirement of a good control strategy is that because motion will never lead to a solution.
The second requirement of a good control strategy is that it be semantic. If its not semantic we may explore a particular useless sequence of operators several times before we finally find a solution. The requirement that a control strategy be semantic corresponds to the need for global motion as well as for local motion.

9. Heuristic Search
Heuristic is a technique that improves the efficiency of a search process possibly by sacrificing claims of completeness.
Heuristic are like tour guides.
They are good to the extent that they point in generally interesting directions.
They are bad to the extent that they miss point of interest to particular individuals.
Some of heurists help to guide a search process without sacrificing any claims to completeness that the process might previously had.
Using good heuristics we can get good solution to hard problem. Heuristic search uses the Heuristic functions for finding the solution of problem.

10. Problem Characteristics
In order to choose the most appropriate method for a particular problem it is necessary to analyze the problem using several key dimensions:
Is the problem decomposable into one of independent smaller or easier sub problem?
Can solution steps be ignored or used.
Is the problem universe predictable
Is the good solution to the problem obvious without comparison to all possible solution
Is the desired solution a state word or a path to a state.
Is a large amount of knowledge absolutely required to solve the problem or knowledge important only to constrain the search.

11. Problem Decomposable

12. Block World Problem

13. Block World Problem(cont..)
Soln. There are some actions given. According to that the robot arm that can manipulate the blocks.
 UNSTACK (A, B): Pick block A from its current position on Block B. The arm must be empty and block A must have no blocks on top of it.
STACK (A, B): Place block A on block B. The arm must already be holding A and the surface of B must be clear.
PICK UP(A): Pickup block A from the table and hold it. The arm must be empty and therefore must be nothing on top of block A.
PUT DOWN (A): Put block A down on the table. The arm must have been holding block A.
ON (A, B): block A is on block B.
ON TABLE (A): block A is on the table.
CLEAR(A): There is nothing on the top of block A
HOLDING(A): The arm is holding block A.
ARM EMPTY: The arm is holding nothing.

14. There are some constraints for solving the problem. They are:
P : Precondition
D : Delete
O : Operation

15. Solve Following

16. Can Solution step be ignored or undone
There are generally three class of problem.
Ignorable (e.g. Theorem proving): In this solution steps can be ignored.
Recoverable (ex. 8 Puzzle) : In this solution step can be undone.
Irrecoverable (ex. Chess) : In this solution steps cannot be undone.
Recoverable problem can be solve by slightly more complicated control strategy, that does some time make mistakes. Back tracking is necessary to recover from such mistake.
Ignorable problem can be solve using simple control structure that never backtracks such control structure is easy to implement.
Irrecoverable problems will need to be solved by a system that expands a great deal of effort making each decision since the decision must be final.

17. Is a Good Solution Absolute or Relative
Let us consider the example of predicate logic:
Marcus was a man.
Marcus was Pompeian.
Marcus was born in 40 A.D.
All men are mortal.
All Pompeian died when the volcano erupted in 79 A.D.
No mortal lives longer than 150 years.
It is now 1991 A.D.
Suppose we ask the question “Is Marcus alive”. The solution of this problem is:

18. Is a Good Solution Absolute or Relative(cont..)
1.  Marcus was a man.
2. All men are mortal.
3. Marcus was born in 40 A.D.
7. It is now 1991 A.D.
9. Marcus’s age 1991 year.
6. No mortal lives longer than 150 years.
10. Marcus was dead.
Or (Relative)
7. It is now 1991 A.D.
5. All Pompeian are dead in 79 A.D.
11. All Pompeian are dead now.
2. Marcus was a Pompeian.
12. Marcus is dead.