I thought about them together thinking about the "doll" concept. For P is something more mechanical, he's a Doll since is missing something, Alice feels like a doll since she was deprived of something. One is following a path to complete himself, the other is evaluating the similar path to escape the inevitable. I imagined this as one day when Alice, returning to her wonderland, noticed a foreign tower from which it was possible to hear an heartbeat, ringing like a bell. She knew it was not from her world, then she saw him. Once she confirmed he was not a threat, she got a confirmation that his destination was that tower and encourage him to go there. This was the first time in which Alice was free from fear, with him was like talking in a neutral land where no war can start, it was a peaceful moment to enjoy.
You can read it here too:
Here's a little chapter about Alice (from AMR) and P (from Lies of P). They encouter in a dream perhaps?
