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Variants of Collapsible Pushdown Systems

Author Pawel Parys



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Pawel Parys

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Pawel Parys. Variants of Collapsible Pushdown Systems. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 500-515, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.CSL.2012.500

Abstract

We analyze the relationship between three ways of generating trees using collapsible pushdown systems (CPS's): using deterministic CPS's, nondeterministic CPS's, and deterministic word-accepting CPS's. We prove that (for each level of the CPS and each input alphabet) the three classes of trees are equal. The nontrivial translations increase n-1 times exponentially the size of the level-n CPS. The same results stay true if we restrict ourselves to higher-order pushdown systems without collapse. As a second contribution we prove that the hierarchy of word languages recognized by nondeterministic CPS's is infinite. This is a consequence of a lemma which bounds the length of the shortest accepting run. It also implies that the hierarchy of epsilon-closures of configuration graphs is infinite (which was already known). As a side effect we obtain a new algorithm for the reachability problem for CPS's; it has the same complexity as previously known algorithms.
Keywords
  • collapsible pushdown systems
  • determinization
  • infinite hierarchy
  • shrink- ing lemma
  • reachability

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