We use symbolic dynamics to study discrete-time dynamical systems withmultiple time delays. We exploit the concept of avoiding sets, which arise fromspecific non-generating partitions of the phase space and restrict theoccurrence of certain symbol sequences related to the characteristics of thedynamics. In particular, we show that the resulting forbidden sequences areclosely related to the time delays in the system. We present two applicationsto coupled map lattices, namely (1) detecting synchronization and (2)determining unknown values of the transmission delays in networks with possiblydirected and weighted connections and measurement noise. The method isapplicable to multi-dimensional as well as set-valued maps, and to networkswith time-varying delays and connection structure.
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