Axiomatizing Rectangular Grids with no Extra Non-unary Relations
Keyword(s):
We construct a first-order formula φ such that all finite models of φ are non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set A ⊆ ℕ is a spectrum of a formula which has only planar models if numbers n ∈ A can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time t(n) and space s(n), where t(n)s(n) ≤ n and t(n); s(n) = Ω(log(n)).
2004 ◽
Vol 18
(16)
◽
pp. 2347-2360
◽
Keyword(s):
1995 ◽
Vol 06
(04)
◽
pp. 395-402
◽
Keyword(s):
Keyword(s):
2000 ◽
Vol 14
(04)
◽
pp. 477-500
2010 ◽
Vol 12
(01)
◽
pp. 85-106
◽