Papers Published

1. Chakrabarty, K; Rayes, JP, Balanced Boolean functions, Iee Proceedings Computers and Digital Techniques, vol. 145 no. 1 (January, 1998), pp. 52-62, Institution of Engineering and Technology (IET) [doi] .
   (last updated on 2022/12/30)

   Abstract:
   Many common logic circuits such as adders, parity checkers and multiplexers realise Boolean functions that are true for exactly half their input combinations, and false for the other half; we refer to such functions as balanced. Recently, these functions have been shown to be very useful for testing logic circuits, and for data encryption in cryptography. Here, we present a general theory of balanced Boolean functions. We derive a necessary and sufficient condition for balance by establishing an equivalence between a balanced function f(X) and a bijection from X to itself. We then analyse the conditions under which functional compositions preserve balance, and examine some specific balance-preserving decompositions. A new characterisation of functional completeness in terms of balance is presented. Finally, we address the problem of counting equivalence classes of balanced functions. ©IEE, 1998.