Piecewise Linerization of Logic Functions

The paper deals with a problem of linearization of multi-output logic functions. Specifically, the case is discussed, when the functions have a large number of variables and cannot be efficiently linearized by using known techniques. For solution of the problem a socalled piecewise linearization is proposed. The piecewise linearization comprises decomposition of an initial multi-output function into a network of components, followed by independent linearization of the components. The decomposition is based on the theory of D -polynomials described in the paper. The resulting piecewise linearized network is directly mapable onto a special type of a binary graph called Parallel Multi Terminal BDD. An efficient heuristic algorithm for the piecewise linearization is provided. The presented benchmarks results demonstrate high efficiency of the proposed method in comparison with known linearization approaches. The results also show that integrating linearization techniques with the described decomposition, thus obtaining the piecewise linearization, are a very promising both from practical and from the theoretical points of view.