The sentences in the examples in Section II. 1 all define regular languages. This is no accident. If we restrict the available numerical predicates appropriately, then the language defined by a monadic second-order sentence is a regular language. Moreover, as we will prove in Theorem III. 1.1 below, every regular language can be defined in this fashion. We will thus obtain a characterization of the regular languages in terms of logic.


Regular Language Finite Automaton Order Type Numerical Relation Peano Arithmetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Howard Straubing
    • 1
  1. 1.Computer Science DepartmentBoston CollegeChestnut HillUSA

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