Motivated by the open question whether TC0 = NC1 we consider the case of linear size TC0. We use the connections between circuits, logic, and algebra, in particular the characterization of TC 0 in terms of finitely typed monoids. Applying algebraic methods we show that the word problem for finite non-solvable groups cannot be described by a FO+MOD+MAJ[REG] formula using only two variables. This implies a separation result of FO[REG]-uniform linear TC0 from linear NC1. © Springer-Verlag Berlin Heidelberg 2009.
CITATION STYLE
Behle, C., Krebs, A., & Reifferscheid, S. (2009). Non-solvable groups are not in FO+MOD+M - AJ2[REG]. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5457, pp. 129–140). https://doi.org/10.1007/978-3-642-00982-2_11
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