Formally, a state is a set of conditions: a state is represented by the set of conditions that are true in it. Transitions between states are modeled by a transition function, which is a function mapping states into new states that result from the execution of actions. Since states are represented by sets of actions, the transition function relative to the STRIPS instance
where 2P is the set of all subsets of P, and is therefore the set of all possible states.
The transition function can be defined as follows, in the assumption that actions can always be executed but they do not have effects if their preconditions are not met (this is a simplifying assumption):
The function
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