Discrete Applied Mathematics 36 (1992) 207

North-Holland 207

Addendum to The threshold order of a Boolean function

Chi Wang and A.C. Williams RUTCOR, Hill Center, Busch Campus, Rutgers University, New Brmswick. NJ 08903, USA

In our paper [2], we claimed to have introduced the notion of the threshold order of a Boolean function, and we went on to develop a number of properties of Boolean functions based on that notion. Professor T. Krishnan of the Indian Statistical Institute has now pointed out to us that this notion was, in fact, first in- troduced by him a quarter century earlier in 1966 [l], using the same terminology. The developments are, however, in quite different directions, and except for the basic result that the threshold order is less than or equal to the dimension, there ap- pears to be no overlap at all. We regret, however, having overlooked this very significant early paper by Professor Krishnan.

References

[l] T. Krishnan, On the threshold order of a Boolean function, IEEE Trans. Electron. Comput. 15

( 1966) 369-372.

[2] C. Wang and A.C. Williams, The threshold order of a Boolean function, Discrete Appl. Math. 31

(1991) 51-69.

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