During the last 20 years, the complexity of solving equations
over finite algebras has been studied also from a universal
algebraic viewpoint. Solving systems of equations can
be seen as a constraint satisfaction problem, which led B.\ Larose
and L.\ Z\'adori to a description of algebras in congruence modular
varieties for which polynomial
systems are solvable in polynomial time. P.\ Mayr has recently
generalized this result to systems of \emph{term equations}.
Sytems over supernilpotent algebras can be seen
as polynomial systems over finite fields, and we give some new
results on the zero sets of such systems (joint work with S. Gr\"unbacher
and P.\ Hametner).
The question whether the solutions of one system are contained
in the solutions of another system leads to the problem of checking
the validity of quasi-identities. We describe the complexity of
this problem for algebras with a Mal'cev term (joint
work with S.\ Gr\"unbacher).
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Forschungs-