Abstract
Following recent works connecting two-variable logic to circuits and monoids, we establish, for numerical predicate sets β satisfying a certain closure property, a one-to-one correspondence between FO[< β]-uniform linear circuits, two-variable formulae with β predicates, and weak block products of monoids. In particular, we consider the case of linear TC 0, majority quantifiers, and finitely typed monoids. This correspondence will hold for any numerical predicate set which is FO[
Cite
CITATION STYLE
Behle, C., Krebs, A., & Mercer, M. (2007). Linear circuits, two-variable logic and weakly blocked monoids. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4708 LNCS, pp. 147–158). Springer Verlag. https://doi.org/10.1007/978-3-540-74456-6_15
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