Logic and Rational Languages of Scattered and Countable Series-Parallel Posets

  • Amazigh Amrane
  • Nicolas BedonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)


We show that an extension of MSO with Presburger arithmetic, named P-MSO, is as expressive as branching automata over scattered and countable N-free posets. As a consequence of the effectiveness of the constructions from one formalism to the other, the P-MSO theory of the scattered and countable N-free posets is decidable.


Automata and logic Transfinite N-free posets Series-parallel posets Series-parallel rational languages Branching automata Monadic second-order logic Presburger arithmetic 



The authors would like to thank all the referees for their helpful comments.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LITIS (EA 4108)Université de RouenRouenFrance

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