n-tuples of 0s and 1s: necessary and sufficient conditions for intrinsic order

Abstract

In an arbitrary stochastic Boolean model we compare the values of a finite set of binary states probabilities, without computing them. The relative positions of 0s and 1s in the binary n-tuples decide by themselves which one has the largest probability. This positional criterion defines an intrinsic order relation in {0,1}(n), which is independent of,the probabilities of the Boolean variables. We obtain different characterizations, as well as necessary conditions and sufficient conditions, for intrinsic order. These propositions explain some relevant properties of the structure of the intrinsic order graph. The results can be applied in many different areas: wherever the random variables of the problem are propositional variables (false or true, i.e: 0 or 1).