Adaptive Synchronisation of Pushdown Automata

Authors A. R. Balasubramanian , K. S. Thejaswini

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A. R. Balasubramanian
  • Technische Universität München, Germany
K. S. Thejaswini
  • Department of Computer Science, University of Warwick, Coventry, UK


We would like to thank Dmitry Chistikov for referring us to previous works on this topic.

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A. R. Balasubramanian and K. S. Thejaswini. Adaptive Synchronisation of Pushdown Automata. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We introduce the notion of adaptive synchronisation for pushdown automata, in which there is an external observer who has no knowledge about the current state of the pushdown automaton, but can observe the contents of the stack. The observer would then like to decide if it is possible to bring the automaton from any state into some predetermined state by giving inputs to it in an adaptive manner, i.e., the next input letter to be given can depend on how the contents of the stack changed after the current input letter. We show that for non-deterministic pushdown automata, this problem is 2-EXPTIME-complete and for deterministic pushdown automata, we show EXPTIME-completeness. To prove the lower bounds, we first introduce (different variants of) subset-synchronisation and show that these problems are polynomial-time equivalent with the adaptive synchronisation problem. We then prove hardness results for the subset-synchronisation problems. For proving the upper bounds, we consider the problem of deciding if a given alternating pushdown system has an accepting run with at most k leaves and we provide an n^O(k²) time algorithm for this problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Problems, reductions and completeness
  • Adaptive synchronisation
  • Pushdown automata
  • Alternating pushdown systems


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