The Number of Canalyzing Functions over Any Finite Set

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In this paper, we extend the
definition of Boolean canalyzing functions to the canalyzing functions of
multi-state case. Namely, *f:Q*^{n}*→**Q* , where *Q={a*_{1}*,a*_{2}*,...,a*_{q}*}* . We obtain its cardinality
and the cardinalities of its various subsets (They may not be disjoint). When *q=**2*, we obtain a combinatorial
identity by equating our result to the formula in [1]. For a better
understanding to the magnitude, we obtain the asymptotes for all the
cardinalities as either* n** →∞* or

References

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doi:10.1016/j.physd.2004.07.002

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