We describe a new way to construct large subdirectly irreducibles within an equational class of algebras. We use this construction to show that there are forbidden geometries of multitraces for finite algebras in residually small equational classes. The construction is first applied to show that minimal equational classes generated by simple algebras of types 2, 3 or 4 are residually small if a...

In classes developed using design-by-contract, contracts contain assertions that formalise preconditions, postconditions and invariants. To be sure that contracts are complete, they can be derived from specifications. For classes in a data structures library, equational specifications are appropriate. However, a conventional equational specification cannot usually be mapped directly to contract...

This paper belongs to our series of works on algebraic geometry over arbitrary structures. In this one, there will be investigated seven equivalences (namely: geometric, universal quasi-equational, universal, elementary, and combinations thereof) in specific classes structures (equationally Noetherian, qω-compact, uω-compact, equational domains, co-domains, etc.). The main questions are the fol...

In this paper we study first-order definability in the lattice of equational theories of commutative semigroups. In a series of papers, J. Ježek, solving problems posed by A. Tarski and R. McKenzie, has proved, in particular, that each equational theory is first-order definable in the lattice of equational theories of a given type, up to automorphism, and that such lattices have no automorphism...

According to Barthelman and Blumensath, the following families of infinite graphs are isomorphic: (1) prefix-recognisable graphs, (2) graph solutions of VR equational systems and (3) MS interpretations of regular trees. In this paper, we consider the extension of prefixrecognisable graphs to prefix-recognisable structures and of graphs solutions of VR equational systems to structures solutions ...

The idea to combine the advantages of function and logic programming has attracted many researches. Their work ranges from the integration of existing languages over higher-order logic to equational logic languages, where logic programs are augmented with equational theories. Recently, it has been proposed to handle those equational theories by complete sets of transformations. These transforma...