In this paper we consider the problem of representing and reasoning about systems, especially probabilistic systems, with hidden state. We consider transition systems where the state is not completely visible to an outside observer. Instead, there are observables that partly identify the state. We show that one can interchange the notions of state and observation and obtain what we call a dual system. In the case of deterministic systems, the double dual gives a minimal representation of the behaviour of the original system. We extend these ideas to probabilistic transition systems and to partially observable Markov decision processes (POMDPs). © 2013 Springer-Verlag.
CITATION STYLE
Dinculescu, M., Hundt, C., Panangaden, P., Pineau, J., & Precup, D. (2013). The duality of state and observation in probabilistic transition systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7758 LNCS, pp. 206–230). https://doi.org/10.1007/978-3-642-36976-6_14
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