Algebraic Analysis of Nondeterministic Behavior

This paper is concerned with the analysis of design errors that lead to unpredictable response of digital systems. Besides classical topics, such as hazards and races, the analysis of malfunctions in real circuits is also included. After defining the notion of behavior and nondeterministic response, a general approach for detecting such design problems through algebraic analysis is presented. Compared with existing simulation methods, the algebraic technique provides results of improved accuracy. Another basic advantage is the ability to accomodate modular synthesis of digital systems. Examples show how the proposed methods deal with sequential circuits under various delay assumptions. In particular, analysis of designs based on nominal delay parameters and on window delays is presented. A novel method, aiming at spike detection, is also presented. The ability of the algebraic analysis to detect errors in a modular design environment is illustrated by means of an example. Finally, the topic of nondeterministic behavior at RTL is briefly discussed. Notably, an algebraic method for deriving setup and hold time constraints from the circuit delay parameters is proposed.