A Logical Descriptor for Regular Languages via Stone Duality

  • Stefano Aguzzoli
  • Denisa Diaconescu
  • Tommaso Flaminio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8687)


In this paper we introduce a class of descriptors for regular languages arising from an application of the Stone duality between finite Boolean algebras and finite sets. These descriptors, called classical fortresses, are object specified in classical propositional logic and capable to accept exactly regular languages. To prove this, we show that the languages accepted by classical fortresses and deterministic finite automata coincide. Classical fortresses, besides being propositional descriptors for regular languages, also turn out to be an efficient tool for providing alternative and intuitive proofs for the closure properties of regular languages.


regular languages finite automata propositional logic Stone duality 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Stefano Aguzzoli
    • 1
  • Denisa Diaconescu
    • 2
  • Tommaso Flaminio
    • 3
  1. 1.Department of Computer ScienceUniversity of MilanItaly
  2. 2.Department of Computer Science, Faculty of Mathematics and Computer ScienceUniversity of BucharestRomania
  3. 3.DiSTA - Department of Theoretical and Applied ScienceUniversity of InsubriaItaly

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