Abstract. Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [LM]. Properties of line digraphs inherited from the source have been studied, for instance in [H] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k, l)-kernels in the context of state splittings and also look at (k, l)-semikernels, k-Grundy functions and their duals.

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