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Universal and Uniform Action Reversibility

The problem of action reversibility studies whether effects of a given action can be reversed (or undone) by a sequence of (other) actions. For example, actions whose effects can be reversed cannot lead to dead-ends. In the usual settings, the problem of action reversibility is PSPACE-complete, that is, as hard as deciding plan existence.

In this paper, we focus on subclasses of the action reversibility problem, universal and uniform action reversibility, where the former considers all states in which the action in question is applicable, while the latter requires a single reverting action sequence, independent of the considered states. Specifically, we study the relations between projection abstractions and the subclasses of the action reversibility problem and we show that universal uniform reversibility of a given action can be decided on projection consisting of only the variables present in the schema of the action in question.