Computing with relational machines.

We propose a relational computing paradigm based on Eilenberg machines, an effective version of Eilenberg's X-machines suitable for general non-deterministic computation. An Eilenberg machine generalizes a finite-state automaton, seen as its control component, with a computation component over a data domain specified as a relational algebra, its actions being interpreted as binary relations over the data domain. We show various strategies for the sequential simulation of our relational machines, using variants of the reactive engine. In a particular case of finite machines, we show that bottom-up search yields an efficient complete simulator. Relational machines may be composed in a modular fashion, since atomic actions of one machine can be mapped to the characteristic relation of other relational machines acting as its parameters. The control components of machines can be compiled from regular expressions. Several such translations have been proposed in the literature, which we briefly survey.