4 problems

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The characterization of fading-memory maps by GUES state-affine systems
Fading-memory realization conjecture. FM maps on infinite sequences are precisely those realizable by GUES SASs, and every such map induces a UF map on finite sequences.
Conjectureopenfading-memory input-output-maps state-space-systemsarXiv posted 2 days ago
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Affine state-space conjecture for affine time-invariant systems
A state variable has the Markovian property that the current state summarizes all relevant past information, so future trajectories depend only on the present state and the current…
Conjectureopenaffine-systems control-theory state-space-systemsarXiv posted 2 days ago
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The generic constancy conjecture for causal stochastic solutions
Generic constancy conjecture. Suppose that $\Pc_{\mathrm{in}}^-$ and $\Pc_{\mathrm{state}}^-$ are Polish and that…
Conjectureopendynamical-systems state-space-systems stochastic-dynamicsarXiv posted 2 days ago
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The finite constant-solution conjecture for deterministic state-space systems
Finite constant-solution conjecture. If $\#\Sc^{\mathrm{det}}(\Seq{u})$ is constant on $\US^-$ and this constant is finite, then the state-space system has the FMP.
Conjectureopendynamical-systems state-space-systemsarXiv posted 2 days ago

The characterization of fading-memory maps by GUES state-affine systems