Decisional States

This article introduces the decisional states of system, and provides a practical algorithm for computing them. The decisional states are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or cost function. The transitions between these decisional states correspond to events that lead to a change of decision. The utility function encodes some a priori knowledge external to the system. The decisional states then take in account both the intrinsic underlying structure of the system (the epsilon-machine) and that external information. An algorithm is provided so as to estimate the states and their transitions from data. Application examples are given for edge-emitting hidden Markov model reconstruction, cellular automata filtering, and edge detection in images.