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Monadic Second-Order Logic with Arbitrary Monadic Predicates

Published: 18 August 2017 Publication History

Abstract

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 very simple proofs that the Straubing Conjecture holds for all fragments of MSO with monadic predicates and that the Crane Beach Conjecture holds for MSO with monadic predicates. The third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.

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  1. Monadic Second-Order Logic with Arbitrary Monadic Predicates

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      Published In

      cover image ACM Transactions on Computational Logic
      ACM Transactions on Computational Logic  Volume 18, Issue 3
      July 2017
      273 pages
      ISSN:1529-3785
      EISSN:1557-945X
      DOI:10.1145/3130378
      • Editor:
      • Orna Kupferman
      Issue’s Table of Contents
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      Publication History

      Published: 18 August 2017
      Accepted: 01 April 2017
      Revised: 01 September 2016
      Received: 01 February 2016
      Published in TOCL Volume 18, Issue 3

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      Author Tags

      1. Automata with advice
      2. monadic predicates
      3. morphic predicates

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      • Alan Turing Institute under the EPSRC
      • French Agence Nationale de la Recherche, AGGREG project

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