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Decision processes with incomplete state feedback have been traditionallymodeled as Partially Observable Markov Decision Processes. In this paper, wepresent an alternative formulation based on probabilistic regular languages.The proposed approach generalizes the recently reported work on languagemeasure theoretic optimal control for perfectly observable situations and showsthat such a framework is far more computationally tractable to the classicalalternative. In particular, we show that the infinite horizon decision problemunder partial observation, modeled in the proposed framework, is$\epsilon$-approximable and, in general, is no harder to solve compared to thefully observable case. The approach is illustrated via two simple examples.

Optimal Control of Infinite Horizon Partially Observable Decision Processes Modeled As Generators of Probabilistic Regular Languages