Algebras for hazard detection

Hazards pulses are undesirable short pulses caused by stray delays in digital circuits. Such pulses not only may cause errors in the circuit operation, but also consume energy, and add to the computation time. It is therefore very important to detect hazards in circuit designs. Two-valued Boolean algebra, which is commonly used for the analysis and synthesis of digital circuits, cannot detect hazard conditions directly. To overcome this limitation several multi-valued algebras have been proposed for hazard detection. This paper surveys these algebras, and studies their mathematical properties. Also, some recent results unifying most of the multi-valued algebras presented in the literature are described. Our attention in this paper is restricted to the study of static and dynamic hazards in gate circuits.