Compositional approach to design of digital circuits

Abstract

In this work we explore compositional methods for design of digital circuits with the aim of improving existing methodoligies for desigh reuse. We address compositionality techniques looking from both structural and behavioural perspectives. First we consider the existing method of handshake circuit optimisation via control path resynthesis using Petri nets, an approach using structural composition. In that approach labelled Petri net parallel composition plays an important role and we introduce an improvement to the parallel composition algorithm, reducing the number of redundant places in the resulting Petri net representations. The proposed algorithm applies to labelled Petri nets in general and can be applied outside of the handshake circuit optimisation use case. Next we look at the conditional partial order graph (CPOG) formalism, an approach that allows for a convenient representation of systems consisting of multiple alternative system behaviours, a phenomenon we call behavioural composition. We generalise the notion of CPOG and identify an algebraic structure on a more general notion of parameterised graph. This allows us to do equivalence-preserving manipulation of graphs in symbolic form, which simplifies specification and reasoning about systems defined in this way, as displayed by two case studies. As a third contribution we build upon the previous work of CPOG synthesis used to generate binary encoding of microcontroller instruction sets and design the corresponding instruction decoder logic. The proposed CPOG synthesis technique solves the optimisation problem for the general case, reducing it to Boolean satisfiability problem and uses existing SAT solving tools to obtain the result.