The Computational Complexity of Monotonicity in Probabilistic Networks

Many computational problems related to probabilistic networks are complete for complexity classes that have few 'real world' complete problems. For example, the decision variant of the inference problem (pr) is PP-complete, the map-problem is NPPP-complete and deciding whether a network is monotone in mode or distribution is CONPPP- complete. We take a closer look at monotonicity; more specific, the computational complexity of determining whether the values of the variables in a probabilistic network can be ordered, such that the network is monotone. We prove that this problem - which is trivially co-NPPP-hard - is complete for the class co-NPNPPP in networks which allow implicit representation.

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