In artificial intelligence, a process known as state space search is used to explore all potential configurations or states of an instance until one with the necessary feature is found.

A state is a time snapshot representing some aspect of the problem. It is common to practise modelling a problem as a state space or a collection of possible states to understand it better. If an operation can change one state into another, then the two states are connected in the set of states' graph.

Because the state space is implicit—a typical state space graph would be too vast to build and maintain in-memory—state space search often deviates from conventional computer science search techniques. Instead, new nodes are created as they are visited and then frequently destroyed. In combinatorial search, a solution can be either the final state or a sequence of states that lead from an initial state to the final state.

Features

• A state space is a set of all possible states that it can reach from the current state. 
• The nodes of a state space represent states, and the arcs connecting them represent actions.
• A path is a set of states and the actions that link them in the state space. 
• A problem's solution is a node in the graph representing all possible states of the problem. 
• Most AI techniques are based on state space representation.

State space representation

State Space Representation consists of identifying an INITIAL STATE (from where to begin) and a GOAL STATE (the final destination) and then following a specific sequence of actions (called States). Let's define each one individually.

• State: AI problems can be represented as a set of well-formed states. A state can be an Initial State, a Goal State, and several other possible states generated by applying rules between them.
• In an Al problem, space refers to the exhaustive collection of all conceivable states.
• Search is a technique that moves from the beginning state to the desired state by applying valid rules while traversing the space of all possible states.
• A search tree is a tree-like depiction of the search issue. The initial state corresponds to the root node of the search tree, which serves as the tree's starting point.
• It provides the agent with a description of all available actions.
• Transition model: A transition model describes what each action does.
• Path Cost is a function that assigns a cost value to each path.
• It is an activity sequence that connects the beginning node to the end node.
• The optimal option is the one with the lowest cost among all alternatives.

Conclusion

State space representation is beneficial in Al issues because it makes it easy to determine the solution path that leads from the beginning state to the objective state. Therefore, the fundamental task is to develop algorithms that can search across the issue space and discover the optimum solution path.