Alternative algorithm for optimisation of Reed–Muller universal logic module networks

Abstract

Reed-Muller universal logic modules (RM-ULMs) can be used as individual modules or as networks to implement RM functions of any number of variables. For a large RM expansion, it is generally more efficient to realise it using cascades of low-order RM-ULMs. A programmed algorithm for the optimisation of the number of modules at the sub-system level has already been published. In the paper an alternative algorithm is presented which performs similar optimisation of fixed-polarity generalised RM expansions but without the need to maintain a saved-branch counter and an input record. Also, whenever the number of piterms having the specific control-tuple-state exceeds two, it is not necessary for the algorithm to perform separate variable examinations. Consequently, the saving in computation time will be especially significant in RM expansions with large number of variables. The resulting algorithm is simple in structure and can be easily implemented using high-level languages such as C or Fortran.