Some non conventional computers [1][2] do exponential space in polynomial time.
[1] Lipton, R. DNA solution of hard computational problems. Science 268 (1995), 542-545.
[2] Head, T. Aqueous Solutions of Algorithmic Problems: Emphasizing Knights on a 3 x 3. Lecture Notes In Computer Science; Vol. 2340
I skimmed [2] and it seems very interesting.
Still, regardless of whether P!=NP, it is known that P is contained in NP which is contained in PSPACE. These classes are defined for certain computational models. If you change the computational model then those definitions might not make sense.
>Some non conventional computers [1][2] do exponential space in polynomial time.
For under $500 ...
Re:GetACoder.com: Solve P Vs NP
by suppressingfire on Monday August 16, 2010 @10:54AM
(#1607925)
As a re-representation of the DNA computing work cited above, you can actually do exponential work in poly time using a photocopier.
EDIT: here's a link to a paper describing this approach: http://www.springerlink.com/content/j5213p8761224304/
Re:GetACoder.com: Solve P Vs NP
by suppressingfire on Monday August 16, 2010 @10:52AM
(#1607915)
Whoa... I never thought I'd see my dad's work reffed on HN.
You can have an algorithm that uses exponential time and only polynomial space, but not the other way around.