III. State Space Search Graph

Augment the labeled graph with a State Space Search graph $($As $02).$

For your reference, consider the following points.

$$ Describe a finite set of states with actions for any given maze configuration $($Extend your work in As$02$ to the area of grids that covers the exits in the given maze$).$

$$ Normalize a standard rule for specifying state representation for four perceived percepts within a grid using the inner states concept. Each percept is represented by a state which contains a $4-$tuple component described in Part I. What is the state representation for grids in which four sides of the grid are open?

$$ Describe the state space search graph associated with the labeled graph $($As$02).$

$$ For each node of the labeled graph, there corresponds to a state that contains four inner states, namely four $4-$tuple components.

$$ For each edge of the labeled graph, there corresponds to an action or state.Actions.

$$ What is the state representation for two adjacent grids, each of the grids has four open sides.

$$ Describe the use of the state space search graph to verify the application of a sequence of actions or state.Actions to traverse the required grids $($percepts vs states$)$ along the edges between nodes. The state space search graph serves as a tool to validate the application of a sequence of actions or state.Actions in navigating through the maze. By traversing the edges between nodes, the graph verifies that the percepts perceived by the agent align with the expected states as determined by the applied actions. Note that each grid also stands for a sequence of percepts taken at a time interval, and only the last percept is considered.

$$ Consider entering $($forward action$)$ each grid. There corresponds to a perceived percept that matches its corresponding inner state of the state for the grid. When executing a forward action to enter each grid, the perceived percept corresponds to the inner state specified for that grid with the state within the state. This ensures consistency between the agent$$s actions and the resulting percepts encountered during traversal.

$$ Consider taking any turn action within the grid, there corresponds to a perceived percept that matches its corresponding state. When taking any turn action within a grid, the perceived percept corresponds to the state specified for that grid. This ensures that the agent$$s actions are accurately reflected in the resulting percepts experienced during traversal.

$$ Describe goal states and goalTEST procedure.

$$ Given a maze with a necessary and sufficient annotation and its corresponding constructed graph, discuss whether the state space search graph can be generated using programming.

$$ Discuss whether the state space search graph serves as a tool for planning and decision$-$making within the learning process. Learning components may use the state space search graph to explore and evaluate different strategies for maze navigation, but the graph itself is not inherently involved in the learning process.

IV$.$ From a Search Graph Augmented with State Space Search Graph

Construct A$*$ or Iterative Deepening A$*($IDA$*),$ but not both.

The agent, consisting of algorithms, traverses a given maze to find an exit.

The graph$$s state space search algorithms for finding the solution are a path from the initial node to the goal node. For your reference, address the following points

$$ Design a general graph search algorithm, a best$-$first strategy A$*$ or IDA$*$ for traversing a given maze configuration to find an exit, with the help from the search graph obtained in Section II$.$

$$ Define Evaluation function f$($n$)=$ g$($n$)+$ h$($n$)$

$$ g$($n$)$ represents the actual cost to reach state n from the initial state.

$$ h$($n$)$ denotes the estimated cost $($distance$)$ from state n to the closest goal.

$$ Describe that A$*$ or IDA$*$ uses an admissible and consistent heuristic in addition to the actual cost to reach state n from the initial state.

$$ Assign g$($n$)$ and h$($n$)$ with cost values for each of the grids$/$nodes of the given maze configuration

$$ Discuss conditions for the optimality: admissibility and consistency

$$ Based on the search graph of the given maze configuration, give a few examples for demonstrating using A$*$ or IDA$*$ search on the labeled graph

$$ Is the A$*$ or IDA$*$ search technique complete, optimal, and heuristic? Justify your claims.

$$ Discuss the time and space efficiency of the A$*$ search and justify your claims.

$$ Define the goal test.