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Languages Defined with Modular Counting Quantifiers
2001
Information and Computation
We prove that a regular language defined by a boolean combination of generalized 1 -sentences built using modular counting quantifiers can be defined by a boolean combination of 1 -sentences in which only regular numerical predicates appear. The same statement, with " 1 " replaced by "first-order," is equivalent to the conjecture that the nonuniform circuit complexity class ACC is strictly contained in NC 1 . The argument introduces some new techniques, based on a combination of semigroup
doi:10.1006/inco.2000.2923
fatcat:oc5wtxnb55gezezhx66qofl2oi