= Solution
Let $V$ be the traversable squares and $H\subseteq V$ the exits. Sample the <state space> at the end of each complete round, so a live state is $s=(r,f)\in V\times V$ with $r\ne f$. The given starting positions specify the initial state. The board and exits are fixed problem data, rather than changing components of the <state space>.
The rabbit has at most five actions: stay or move to one of its traversable orthogonally adjacent squares. A <search transition model> first applies that action, giving $r'$, and immediately checks for capture at $r'=f$. Otherwise hold $r'$ fixed and apply the fox rule twice, checking for capture after each step. A capture is terminal failure; it must not be overlooked merely because the fox could subsequently move elsewhere. A surviving successor is $(r',f'')$. Equivalently, omit actions whose complete-round outcome is capture.
The <goal test> is \b[the rabbit is on an exit after surviving the fox's entire turn]: $r'\in H$ and no capture occurred in that round. Merely entering an exit before the fox moves is insufficient. Each surviving <search transition model> step has cost one when minimizing rounds.
Only legal moves are considered when applying the stated horizontal preference: try a legal horizontal step that reduces horizontal separation, otherwise a legal vertical step that reduces vertical separation, otherwise stay. If a blocked preferred direction is instead interpreted as forcing a stay immediately, the counterexamples below and all completeness and optimality conclusions remain valid.
Back to article page
