Past exam of the computer science course of the University of Oxford / 2021 / Artificial intelligence / 3 / c / Solution

There are $G=2mn+n(n-1)$ distinct ground actions, or $tG$ time-indexed action variables over $t$ transition steps. Each of STRIPS's pick and drop action schemas has $mn$ type-correct instantiations. A move chooses an ordered pair of distinct buckets, giving $n(n-1)$. Every physical action is a ground action before it receives a time index in SATPlan.These counts exclude static type checks after action grounding and exclude optional persistence/no-op action symbols. Using successor-state axioms supplies persistence without separate no-op action variables. If one action occurrence is allowed per layer, it is selected from the same ground-action set; a parallel encoding also begins with these physical ground actions, but has a different exclusion policy.