A survey on the arity gap

Journal of Multiple-Valued Logic and Soft Computing, 24 (2015), 223–249
http://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-24-number-1-4-2015/mvlsc-24-1-4-p-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.