An algebraic model for asynchronous circuits verification

Abstract

An algebraic methodology for comparing switch-level circuits with higher-level specifications is presented. Switch-level networks, 'user' behavior, and input constraints are modeled as asynchronous machines. The model is based on the algebraic theory of characteristic functions (CF). An asynchronous automation is represented by a pair of CFs, called a dynamic CF (DCF): the first CF describes the potential stable states, and the second CF describes the possible transitions. The set of DCFs is a Boolean algebra. Machine composition and internal variables abstraction correspond, respectively, to the product and sum operations of the algebra. Internal variables can be abstracted under the presence of a domain constraint. The constraint is validated by comparison to the outside behavior. The model is well suited for speed-independent circuits for which the specification is given as a collection of properties. Verification reduces to the validation of Boolean inequalities.