 Some heuristic algorithms such as A* can be proven optimal provided that the heuristic they use is monotonic.In Boolean algebra, a monotonic function is one such that for all "a""i" and "b""i" in {0,1}, if "a"1 ≤ "b"1, "a"2 ≤ "b"2, ..., "a""n" ≤ "b""n" (i.e.the Cartesian product {0, 1}"n" is ordered coordinatewise), then f("a"1, ..., "a""n") ≤ f("b"1, ..., "b""n").