X-Nico

unusual facts about decision problem


Decision problem

However, this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for example, the complexity of the characteristic functions of an NP-complete problem and its co-NP-complete complement is exactly the same even though the underlying decision problems may not be considered equivalent in some typical models of computation.


Pseudorandom generator

In 1997 Russell Impagliazzo and Avi Wigderson proved that the construction of Nisan and Wigderson is a pseudorandom generator assuming that there exists a decision problem that can be computed in time 2O(n) on inputs of length n but requires circuits of size 2Ω(n).


see also

Post canonical system

Emil Post, "Formal Reductions of the General Combinatorial Decision Problem," American Journal of Mathematics 65 (2): 197-215, 1943.