Regular languages defined with generalized quantifiers

  • Howard Straubing
  • Denis Thérien
  • Wolfgang Thomas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


We study an extension of first-order logic obtained by adjoining quantifiers that count with respect to an integer modulus. It is shown that the languages definable in this framework are precisely the regular languages whose syntactic monoids contain only solvable groups. We obtain an analogous result for regular ω-languages and establish some connections with complexity theory for fixed-depth families of circuits.


Solvable Group Atomic Formula Regular Language Word Structure Infinite Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Howard Straubing
    • 1
  • Denis Thérien
    • 2
  • Wolfgang Thomas
    • 3
  1. 1.Computer Science DepartmentBoston CollegeChestnut HillUSA
  2. 2.School of Computer ScienceMcGill UniversityMontréalCanada
  3. 3.Lehrstuhl für Informatik IIRWTH AachenAachenWest Germany

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