Lewis and Coates have written an excellent book on threshold logic. Throughout, specific examples precede and follow the presentation of theorems and procedures.
In the first three chapters, the authors introduce threshold gate and other preliminary properties of threshold functions and networks. This is a good introduction to the subject. It is followed by a clear presentation of the synthesis procedures developed by the authors, although it might have been more beneficial to the reader had other available procedures been given more adequate coverage.
The synthesis of switching functions with three input majority gates is lucidly presented, and was quite interesting to this reviewer because such networks are more practically feasible.
Next, the authors clearly demonstrate how to make use of the concept of dual functions and properties of dual functions for the realization of switching functions with threshold gates. The function tree is used here to test the linear separability of a given switching function and to obtain maximally reliable realization, if it is linearly separable.
Methods of solving simultaneous inequalities, with major emphasis on the application of linear programming, follow advantageously the book's initial material. The presentation is clear and concise. There are, however, many other sources for a more thorough treatment of linear programming.
In the final section a sequential procedure is introduced to obtain singlegate realizations for linearly separable functions. The treatment is quite good. There are no problem sets given, and the bibliography is rather complete through 1965. This reviewer recommends the book highly.