Prefix Rewriting for Nested-Words and Collapsible Pushdown Automata

  • Christopher Broadbent
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)


We introduce two natural variants of prefix rewriting on nested-words. One captures precisely the transition graphs of order-2 pushdown automata and the other precisely those of order-2 collapsible pushdown automata (2-CPDA). To our knowledge this is the first precise ‘external’ characterisation of 2-CPDA graphs and demonstrates that the class is robust and hence interesting in its own right. The comparison with our characterisation for 2-PDA graphs also gives an idea of what ‘collapse means’ in terms outside of higher-order automata theory. Additionally, a related construction gives us a decidability result for first-order logic on a natural subclass of 3-CPDA graphs, which in some sense is optimal.


Decidability Result Regular Language Transition Graph Tree Automaton Recursion Scheme 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christopher Broadbent
    • 1
  1. 1.LIAFA (CNRS and Paris 7)ParisFrance

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