Even faster algorithms for CSAT over~supernilpotent algebras

Abstract: In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is probabilistic with linear time complexity. Application of the former algorithm to finite groups provides time complexity that is usually lower than in previously best (given by F\"oldv\'ari) and application of the latter leads to corollary, that circuit satisfiability problem for group G is either tractable in probabilistic linear time if G is nilpotent or is NP-complete if G fails to be nilpotent. The results are obtained, by translating equations between polynomials over supernilpotent algebras to bounded degree polynomial equations over finite fields.