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How are actors and agents represented?

title: 'Figure 6: Accuracy and thinking tokens vs. problem complexity for reasoning models across puzzle environments. As complexity increases, reasoning models initially spend more tokens while accuracy declines gradually, until a critical point where reasoning collapses—performance drops sharply and reasoning effort decreases.'

In the River Crossing puzzle described in the text, actors and agents are represented using specific notation. Actors are denoted by symbols such as a1, a2, ..., aN, while agents are represented by symbols A1, A2, ..., AN. This structured representation is essential for clarifying the roles of each individual involved in the puzzle's constraints and actions, highlighting the coordination required for solving the problem.

The problem emphasizes that actors cannot be in the presence of another agent without their own agent present. This means that solving the puzzle necessitates careful planning to ensure safety constraints are maintained throughout the crossing process, thereby introducing complexity to the task at hand[1].


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