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A common problem encountered in many application scenarios is how to represent some prior knowledge about a system in order to determine its true state as efficiently as possible. The information is typically in the form of tests, or questions about the system. Each test can potentially reduce our uncertainty about the system's state. The problem is to represent the information capturing the dependence between tests, their outcomes, and possible states in an efficiently navigable way to aid diagnosis. The most common such representation is a flowchart with leaf nodes corresponding to possible states, and non-leaf nodes corresponding to tests about the state. The problem with flowcharts is that they are notoriously difficult to maintain. Additional knowledge often has to be manually integrated as the system changes, making it impossible to keep track of all possible decision paths, let alone optimize the flow to maximize performance. We propose an efficient method for optimizing an existing flowchart based on a conversion to an auxiliary matrix representation. The main goal of the paper is show a synergy between the two representations in the hope that this will help practitioners choose a better strategy for their applications. We show that such a conversion suggests ways to improve both representations - ways that were not envisioned when using each representation alone. Finally, we show that the two representations are informationally equivalent in the sense that one can be transformed into the other so that if both are used as black-boxes, one would not be able to tell them apart, regardless of which state the system is in.