Relation Algebras can Tile

Abstract Undecidability of the equational theory of the class RA of relation algebras can easily be proved using the undecidability of the word-problem for semigroups. With some effort and ingenuity, one can push this proof through for the larger class SA . We provide another “cause” for undecidability which works for even larger classes than SA . The reason is that we can encode the tiling problem. In doing so we will meet very simple BAO-varieties with undecidable equational theories which might be useful in other undecidability proofs. Our work is part of the research project which tries to establish the border between undecidability and decidability in relational type algebras, cf. [15] , [16] , [12] , [1] and the references therein. The ultimate goal of this research is to come up with versions of relational algebra which are still suitable for modern dynamic applications but whose equational theory is decidable or even tractable.