Relational Algebra as formalism for Hardware Design

This paper introduces relational algebra as an elegant formalism to describe hardware behaviour. Hardware behaviour is modelled by functions that are represented by sets of tables. Relational algebra, developed for designing large and consistent databases is capable to operate on sets of tables and hence on sets of hardware behaviour functions. It pairs the advantages of formal design, such as verification and provable correct designs, to relative ease and simplicity of description. Descriptions tend to be directly mappable to hardware components such as PLA's. This in contrast to other, most predicate based, formal methods that create long and complex descriptions of hardware which make automated theorem provers a necessity for design tasks of practical sizes. Relational algebra can be applied for both combinatorial as sequential designs and also for transformations between designs. We demonstrate the power of this formalism by means of the Mealy to Moore transformation and show that it takes only a few operations.