Reversible Shrinking Two-Pushdown Automata

  • Holger Bock Axelsen
  • Markus Holzer
  • Martin Kutrib
  • Andreas Malcher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9618)


The deterministic shrinking two-pushdown automata characterize the deterministic growing context-sensitive languages, known to be the Church-Rosser languages. Here, we initiate the investigation of reversible two-pushdown automata, RTPDAs, in particular the shrinking variant. We show that as with the deterministic version, shrinking and length-reducing RTPDAs are equivalent. We then give a separation of the deterministic and reversible shrinking two-pushdown automata, and prove that these are incomparable with the (deterministic) context-free languages. We further show that the properties of emptiness, (in)finiteness, universality, inclusion, equivalence, regularity, and context-freeness are not even semi-decidable for shrinking RTPDAs.


Unconventional models of computation Reversible computing Shrinking two-pushdown automata Church-Rosser languages 



The authors acknowledge partial support from COST Action IC1405 Reversible Computation. H. B. Axelsen was supported by the Danish Council for Independent Research \(\mid \) Natural Sciences under the Foundations of Reversible Computing project, and by an IC1405 STSM (short-term scientific mission) grant.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Holger Bock Axelsen
    • 1
  • Markus Holzer
    • 2
  • Martin Kutrib
    • 2
  • Andreas Malcher
    • 2
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagen EDenmark
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

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