Deciding Regular Intersection Emptiness of Complete Problems for PSPACE and the Polynomial Hierarchy

  • Demen GülerEmail author
  • Andreas Krebs
  • Klaus-Jörn Lange
  • Petra Wolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)


For a regular set R of quantified Boolean formulae we decide whether R contains a true formula. We conclude that there is a PSPACE-complete problem for which emptiness of intersection with a regular set is decidable. Furthermore, by restricting depth and order of quantification we obtain complete problems for each level of the polynomial hierarchy with this decidability as well.


Automata and logic Emptiness of regular intersection Quantified Boolean formula PSPACE Polynomial hierarchy 



We thank Benjamin Gras for the fruitful discussions during the TüFTLeR seminar. Also, we give our thanks to Michaël Cadilhac, Silke Czarnetzki and Michael Ludwig for proof-reading.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Demen Güler
    • 1
    Email author
  • Andreas Krebs
    • 1
  • Klaus-Jörn Lange
    • 1
  • Petra Wolf
    • 1
  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

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