Equations over finite algebras

Description

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).

Period	31 May 2024
Event title	AAA105 - 105th Workshop on General Algebra
Event type	Conference
Location	Czech RepublicShow on map