Read-once Projections and Formal Circuit Verification with Binary Decision Diagrams

Computational complexity is concerned with the complexity of solving problems and computing functions and not with the complexity of verifying circuit designs. The importance of formal circuit veriication is evident. Therefore, a framework of a complexity theory for formal circuit veriication with binary decision diagrams is developed. This theory is based on read-once projections. For many problems it is determined whether and how they are related with respect to read-once projections. It is proved that multiplication can be reduced to squaring but squaring is not a read-once projection of multiplication. This perhaps surprising result is discussed. For most of the common binary decision diagram models of polynomial size complete problems with respect to read-once projections are described. But for the class of functions with polynomial-size free binary decision diagrams (read-once branching programs) no complete problem with respect to read-once projection exists.