Ordered Tree-Pushdown Systems

Authors Lorenzo Clemente, Pawel Parys, Sylvain Salvati, Igor Walukiewicz



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Lorenzo Clemente
Pawel Parys
Sylvain Salvati
Igor Walukiewicz

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Lorenzo Clemente, Pawel Parys, Sylvain Salvati, and Igor Walukiewicz. Ordered Tree-Pushdown Systems. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 163-177, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.FSTTCS.2015.163

Abstract

We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine machine, and ordered annotated multi-pushdown systems. In each case, our procedure yields tight complexity.
Keywords
  • reachability analysis
  • saturation technique
  • pushdown automata
  • ordered pushdown automata
  • higher-order pushdown automata
  • higher-order recursive sche

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