Monotone complexity of a pair

Abstract

We define monotone complexity KM(x, y) of a pair of binary strings x,y in a natural way and show that KM(x, y) may exceed the sum of the lengths of x and y (and therefore the a priori complexity of a pair) by αlog(|x| + |y|) for every α < 1 (but not for α > 1). We also show that decision complexity of a pair or triple of strings does not exceed the sum of its lengths. © 2010 Springer-Verlag.