1,473 research outputs found
Decidability in the logic of subsequences and supersequences
We consider first-order logics of sequences ordered by the subsequence
ordering, aka sequence embedding. We show that the \Sigma_2 theory is
undecidable, answering a question left open by Kuske. Regarding fragments with
a bounded number of variables, we show that the FO2 theory is decidable while
the FO3 theory is undecidable
White noise theory of robust nonlinear filtering with correlated state and observation noises
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling the state process as the solution of a (stochastic) differential equation with a finitely additive white noise as the input. This makes it possible to introduce correlation between the state and observation noise, and to obtain robust nonlinear filtering equations in the correlated noise cas
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