Monadic Second-Order Logic with Arbitrary Monadic Predicates

  • Nathanaël Fijalkow
  • Charles Paperman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8634)


We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent characterizations. We consider the regularity question: given a language in this class, when is it regular? To answer this, we show a substitution property and the existence of a syntactical predicate.

We give three applications. The first two are to give simple proofs of the Straubing and Crane Beach Conjectures for monadic predicates, and the third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.


Regular Language Predicate Symbol Circuit Complexity Boolean Circuit Substitution Property 
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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Nathanaël Fijalkow
    • 1
    • 2
  • Charles Paperman
    • 1
  1. 1.LIAFAParis 7France
  2. 2.University of WarsawPoland

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