eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-13
17:1
17:15
10.4230/LIPIcs.CONCUR.2021.17
article
Adaptive Synchronisation of Pushdown Automata
Balasubramanian, A. R.
1
https://orcid.org/0000-0002-7258-5445
Thejaswini, K. S.
2
Technische Universität München, Germany
Department of Computer Science, University of Warwick, Coventry, UK
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol203-concur2021/LIPIcs.CONCUR.2021.17/LIPIcs.CONCUR.2021.17.pdf
Adaptive synchronisation
Pushdown automata
Alternating pushdown systems