# Meaning of P=NP? depends on space-time geometry ?

This question is about Page 125 of the book "Cellular automata in hyperbolic spaces: Volume 2" By Maurice Margenstern, Publisher Archives contemporaines, 2008.

In the author's opinion, the question P=NP is ill-posed because in the hyperbolic setting P=NP or in the notation used later in the book Ph=NPh.

I don't know enough about complexity to know what to make of this, but it sounds interesting.

So the question is basically, what do you make of it?

Do his claims make sense ?

And if you look later in the book, the author defines P$_h$ as problems solvable in polynomial time on a hyperbolic cellular automaton, and proves P$_h$=PSPACE (and NP$_h$=P$_h$=PSPACE), so even the author isn't really taking complexity classes to change in hyperbolic space.
• That's why I said "appears to change" rather than "changes". The same is true with hyperbolic space; we don't know that P$\neq$PSPACE, although that's less uncertain than P$\neq$BQP. – Peter Shor Oct 31 '10 at 17:01