Relation Algebras Can Tile
Maarten Marx
Abstract:
Abstract Undecidability of the equational theory of the class RA of
relation algebras can easily be proved using the undecidability of
the wordproblem 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 (N'emeti, 1987), (Maddux, 1994), (Andr'eka et al., 1995)
and the references therein, (Marx, 1995). 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.
To appear in `Information Science'.