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IMA Journal of Mathematical Control and Information 1991 8(1):45-80; doi:10.1093/imamci/8.1.45
© 1991 by Institute of Mathematics and its Applications
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Classical and Logic-Based Dynamic Observers for Finite Automata

PETER E. CAINES, RUSSELL GREINER and SUNING WANG

Department of Electrical Engineering, McGill University 3480 University Street, Montreal, P.Q., H3A 2A7 Canada and Canadian Institute for Advanced Research
Department of Computer Science, University of Toronto 10 Kings College Rd. Ont., M5S 1A4, Canada
Department of Electrical Engineering, McGill University 3480 University St. Montreal, P.Q., H3A 2A7 Canada

This paper formulates the state estimation problem for a partially observed input-state-output (N-state) automation in terms of a classical observer automaton each of whose nodes correspond to the set of states consistent with a particular sequence of observations. It next provides several complexity results about these observers, i.e. bounds their convergence time and sizes, by use of the associated directed acyclic observer. The final part introduces the notion of a logic-based dynamic observer, shows how to encode these observers in predicate calculus, demonstrates an equivalence between classical and logic-based systems and observers, and illustrates some of the advantages of the logic-based approach.


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