Modeling repetitive behavior
A recent conversation with Didier Demolin about animal vocalizations motivated me to return to a an issue discussed in "Finch linguistics", 7/15/2011. (See also "Markov's heart of darkness", 7/18/2011, "Non-Markovian yawp", 9/18/2011, and "The long get longer", 12/4/2013.)
The point is this: In modeling the structure of simple repetitive behavior, considerations from (traditional) formal language theory can obscure rather than clarify the issues. These threats to insight include the levels of the Chomsky-Schützenberger hierarchy, the "recursion" controversy, and so on.
What follows is an attempt at a simple illustrated explanation.
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