A

The *quasiequational theory* of a class of structures is the set of quasiequations that hold in all members of the class.

The *decision problem* for the quasiequational theory of a class of structures is the problem with input: a quasiequation
of length *n* (as a string) and output: "true" if the quasiequation holds in all members of the class, and "false" otherwise.

The quasiequational theory is *decidable* if there is an algorithm that solves the decision problem, otherwise it is *undecidable*.

The complexity of the decision problem (if known) is one of PTIME, NPTIME, PSPACE, EXPTIME, ...

A complete deductive system for quasiequations is given in [A. Selman,
*Completeness of calculi for axiomatically defined classes of algebras*,
*Algebra Universalis***2**
(1972)
20--32
MRreview].
Additional information on quasiequations can be found e.g. in
[Stanley N. Burris and H.P. Sankappanavar, A Course in Universal Algebra].