Strictness of the Collapsible Pushdown Hierarchy

  • Alexander Kartzow
  • Paweł Parys
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


We present a pumping lemma for each level of the collapsible pushdown graph hierarchy in analogy to the second author’s pumping lemma for higher-order pushdown graphs (without collapse). Using this lemma, we give the first known examples that separate the levels of the collapsible pushdown graph hierarchy and of the collapsible pushdown tree hierarchy, i.e., the hierarchy of trees generated by higher-order recursion schemes. This confirms the open conjecture that higher orders allow one to generate more graphs and more trees.

Full proofs can be found in the arXiv version[10] of this paper.


Context Free Grammar Recursion Scheme Pushdown Automaton Collapsible System Monadic Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Kartzow
    • 1
  • Paweł Parys
    • 2
  1. 1.Universität LeipzigLeipzigGermany
  2. 2.University of WarsawWarszawaPoland

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