Confusion-Tolerant Computation of Probability in Acyclic Nets

This paper presents a solution to the issue of how to compute probabilities in nets with confusion, where confusion is interference between concurrent choices of which enabled transition to perform. A formal framework is developed – using a novel formula based on event weights – for computing the probabilities of execution traces of an acyclic net, which in turn are used to compute the probabilities of the markings, steps, and nodes of the net. We prove the framework satisfies generic probability requirements. We also prove the formula simplifies to the standard formula for computing the probability of independent concurrent events in confusion-free concurrent simple acyclic nets with choice, in the maximally concurrent and interleaving models of concurrency.