Proceedings of the 42nd IEEE International Symposium on Multiple-Valued Logic (ISMVL 2012), IEEE Computer Society, Los Alamitos, (2012), 268-273 http://dx.doi.org/10.1109/ISMVL.2012.11

We propose a parametrized version of arity gap. The parametrized arity gap gap(f,l) of a function f: An -> B measures the minimum decrease in the number of essential variables of f when l consecutive identifications of pairs of essential variables are performed. We determine gap(f,l) for an arbitrary function f and a positive integer l. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions.

CEMAT - Center for Computational and Stochastic Mathematics