Problem formulation

Given a goal to achieve problem formulation is the process of deciding what States to be considered and what actions to be taken to achieve the goal. This is the first step to be taken by any problem solving agent.

State space: State space of a problem is set all of all the states reachable from the initial state by executing any sequence of actions. State is representation of all possible outcomes.

The state space specifies the relation among various problem states thereby, forming a directed network or graph in which the nodes are states and the links between nodes represent actions.

Path: A path is a sequence of states connected by sequence of actions, in a given state space.

Well-Defined Problems and Solutions problems can be defined formally using 5 components as follows:

a. Initial state, b. Actions, c. Successor function , d. goal test, e. Path cost

a. Initial state: The initial state is the one in which the agent starts in.

b. Actions: It is the set of actions that can be executed or applicable in all possible states. A description of what is each action does; the formal name for this is the transition model.

c. Successor function: It is a function that returns a current state on executing an action on the current state.

d. Goal test: It is a test to determine whether the current state is a goal state. In some problems the goal test can be carried out just by comparing current state with the defined goal state, called as explicit goal test. Whereas, in some of the problems that cannot be defined explicitly but needs to be generated by carrying out some computations, it is called as an implicit goal test.

e. Path cost: It is simply cost associated with each step to be taken to reach to the goal state.