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On the Number of Multivalued Switching Functions Realizable by Cascades | IEEE Journals & Magazine | IEEE Xplore

On the Number of Multivalued Switching Functions Realizable by Cascades


Abstract:

Butler [6] gave recurrence relations for computing the number Nr(n) of r-valued (r ≥ 2) switching functions of n variables realizable by a cascaded network of n - 1 r-val...Show More

Abstract:

Butler [6] gave recurrence relations for computing the number Nr(n) of r-valued (r ≥ 2) switching functions of n variables realizable by a cascaded network of n - 1 r-valued cells. The cascades are assumed to have a fixed-input variable assignment. In this correspondence similar recurrence relations are presented for the number Mr(n) of such cascade realizable functions that depend on all n input variables. In particular, for the ternary valued case, explicit formulas for N3(n) and M3(n) are given. Some asymptotic properties of Nr(n) and Mr(n) are also derived, which show that their growth is asymptotically exponential as n increases.
Published in: IEEE Transactions on Computers ( Volume: C-28, Issue: 5, May 1979)
Page(s): 371 - 374
Date of Publication: 31 May 1979

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