Abstract
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.
Supported by La Fondation Sciences Mathématiques de Paris and by the project AMIS (ANR 2010 JCJC 0203 01 AMIS) Full version: mjolnir.cs.ox.ac.uk/~chrb/isophilic.pdf
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Broadbent, C. (2012). Prefix Rewriting for Nested-Words and Collapsible Pushdown Automata. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_17
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DOI: https://doi.org/10.1007/978-3-642-31585-5_17
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