A Process Algebra Foundation for Reasoning about Core ELLA

Abstract

A process algebraic foundation has been developed for formal analysis of synchronous hardware designs represented through the commercially available hardware design language, ELLA. An underlying semantic foundation, based on input/output trace sets, is presented first through the use of state machines. Such a representation enables direct application of standard, fully automated trace equivalence checking tools. However, to overcome the computational limitations imposed by such analysis methods, the input/ output trace semantics is represented through a synchronous process algebra, EPA. Primitive processes in EPA denote the behaviour of primitive hardware components, such as delays or multiplexers, with composition operators corresponding to the different ways in which behaviours may be built. Of particular significance is the parallel composition operator which captures the machinery for building networks from other components/networks. Actions in EPA are structured and signify the state of input and output signals. This structure, however, is abstracted by developing an algebra for the actions. In particular, parallel composition on processes neatly lifts to a special (synchronous) product operation on actions. The EPA representation forms a good basis for semi-automated high-level symbolic manipulation and reasoning tools. First, the original design structure can be maintained, thus easing the problems of user level feedback from tools. Secondly, the application of EPA to ELLA enables a deterministic finite automation form for EPA terms. This provides a route to tractable symbolic verification and simulation, using a state evolution method to establish strong bisimulation properties. The method has been successfully applied to classes of unbounded state space systems.