Problem space hypothesis refers to the idea that problem solving is isomorphic to a search through a mental graph, with nodes corresponding to every possible state of affairs of a problem and connections corresponding to legal moves.
The problem space hypothesis is a psychological theory that suggests that problemsolving involves the creation and manipulation of mental representations, or problem spaces, in the mind. According to this theory, problemsolving involves three stages: problem representation, problem solution, and problem evaluation.
In the problem representation stage, individuals create a mental representation of the problem space, which includes the initial state, goal state, and possible operators or actions that can be taken to reach the goal state. The problem solution stage involves searching for and applying appropriate operators to move from the initial state to the goal state. Finally, in the problem evaluation stage, individuals evaluate whether the solution is correct and efficient.
Here are some examples of how the problem space hypothesis applies to realworld problemsolving situations:

Sudoku puzzles: When solving a Sudoku puzzle, individuals must create a mental representation of the puzzle's problem space, including the initial state (the partially filledin grid), the goal state (a completely filledin grid), and the possible operators (filling in numbers in the empty squares) that can be taken to reach the goal state.

Cooking a meal: When cooking a meal, individuals must create a mental representation of the problem space, including the initial state (the ingredients and equipment on hand), the goal state (a finished, tasty meal), and the possible operators (chopping, sautéing, baking, etc.) that can be taken to reach the goal state.

Building a birdhouse: When building a birdhouse, individuals must create a mental representation of the problem space, including the initial state (a pile of wood and tools), the goal state (a completed birdhouse), and the possible operators (cutting wood, nailing pieces together, sanding, painting, etc.) that can be taken to reach the goal state.
The problem space hypothesis is an important concept in the field of cognitive psychology and has been applied to a range of problemsolving situations, including mathematical problemsolving, scientific reasoning, and creative problemsolving.
To further explore the problem space hypothesis, it is important to understand how it differs from other problemsolving theories, such as the Gestalt approach and the meansend analysis.
The Gestalt approach suggests that problemsolving involves restructuring the problem to create a new perspective. This approach emphasizes the importance of insight and creativity in problemsolving. In contrast, the problem space hypothesis emphasizes the creation and manipulation of mental representations of the problem.
The meansend analysis approach suggests that problemsolving involves breaking the problem down into subgoals and working towards achieving each subgoal. This approach emphasizes the importance of planning and strategy in problemsolving. While the problem space hypothesis also involves planning and strategy, it emphasizes the creation and manipulation of the mental representations of the problem.
Research has supported the problem space hypothesis and its importance in problemsolving. For example, studies have shown that individuals who are better able to create and manipulate mental representations of problems tend to be better problem solvers. Additionally, research has shown that problemsolving performance can be improved through training in mental representation techniques.
The problem space hypothesis has also been applied to realworld problemsolving situations beyond those mentioned above. For example, it has been applied to medical problemsolving, such as diagnosing patients and developing treatment plans. In this context, mental representations of the patient's symptoms, medical history, and possible treatment options are created and manipulated to develop an effective treatment plan.
Overall, the problem space hypothesis is a useful framework for understanding how individuals solve problems. By emphasizing the importance of mental representations and their manipulation, this theory can help individuals improve their problemsolving skills and approach complex problems more effectively.