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A survey on the arity gap

Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás

Journal of Multiple-Valued Logic and Soft Computing, 24 (2015), 223–249

The arity gap of a function of several variables is defined as the minimum decrease in the number of essential variables when essential variables of the function are identified. We present a brief survey on the research done on the arity gap, from the first studies of this notion up to recent developments, and discuss some natural extensions and related problems.