Preparing Relational Algebra for "Just Good Enough" Hardware

Device miniaturization is pointing towards tolerating imperfect hardware provided it is “good enough”. Software design theories will have to face the impact of such a trend sooner or later. A school of thought in software design is relational : it expresses specifications as relations and derives programs from specifications using relational algebra. This paper proposes that linear algebra be adopted as an evolution of relational algebra able to cope with the quantification of the impact of imperfect hardware on (otherwise) reliable software. The approach is illustrated by developing a monadic calculus for component oriented software construction with a probabilistic dimension quantifying (by linear algebra) the propagation of imperfect behaviour from lower to upper layers of software systems.