Languages Defined with Modular Counting Quantifiers

Howard Straubing
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
more » ... and Ramsey theory, which may shed some light on the general case. C
doi:10.1006/inco.2000.2923 fatcat:oc5wtxnb55gezezhx66qofl2oi