State space consists of **all the problem solving tasks**.

**State space:** A state space consists of all the states ,set of operators that shifts from one state to another.

States are also known as **nodes** in a connected graph and the edges are denoted as **operators**. Problem solving can be formulated as search in state space. For example to find the solution of an 8 puzzle game which is represented as **3*3 matrix**.

1 | 2 | 3 |

4 | 5 | |

6 | 7 | 8 |

One of the tile is unoccupied by moving this tile to other positions we can create new states. For example if I move this unoccupied block to right then it becomes

1 | 2 | 3 |

4 | 5 | |

6 | 7 | 8 |

New state

Here we can **create ‘n’ number of states**. The number of new states generated all together constitutes to a state space.

All of these states of the domain and all of these operators. In this case it could be **4 operators** they are the tile can move towards right, left ,up and down. All these operators together constitute to asset of operators. Once the set of operators and actions are defined then move on to finding solution.

For suppose there are two states start state and end state. If the path from start state to end state is found then the problem is solved. State space is defined as the set of all possible configurations that one get from the relevant objects. This is also referred to problem space.

Let us take previous **example 3*3 matrix **having 8 elements and one empty space. This empty space is a problem state. Suppose the first matrix is start and the second is destination, the path from ‘S’ to ’D’ the total number of configurations is 9!.

1 | 2 | 3 |

4 | 5 | |

6 | 7 | 8 |

Start state ‘S’

1 | 2 | 3 |

8 | 4 | |

7 | 6 | 5 |

Destination State ‘D’