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Chistikov, Dmitry, Martyugin, Pavel and Shirmohammadi, Mahsa (2019) Synchronizing automata over nested words. Journal of Automata, Languages and Combinatorics, 24 (2-4). pp. 219-251. doi:10.25596/jalc-2019-219
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Official URL: https://doi.org/10.25596/jalc-2019-219
Abstract
We extend the concept of a synchronizing word from deterministic finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i. e., takes the NWA from all control states to a single control state.
We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound
makes a connection to pebble games and Strahler numbers, and the lower bound goes via small-cost synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete. We also characterize the complexity of a number of related problems, using the observation that the intersection nonemptiness problem for NWA
is EXP-complete.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||||
| Divisions: | Faculty of Science > Computer Science | ||||||
| Library of Congress Subject Headings (LCSH): | Machine theory, Formal languages, Mathematical linguistics | ||||||
| Journal or Publication Title: | Journal of Automata, Languages and Combinatorics | ||||||
| Publisher: | Institut für Informatik · Justus-Liebig-Universität Giessen | ||||||
| ISSN: | 1430-189X | ||||||
| Official Date: | 2019 | ||||||
| Dates: |
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| Date of first compliant deposit: | 28 June 2019 | ||||||
| Date of first compliant Open Access: | 30 June 2020 | ||||||
| Volume: | 24 | ||||||
| Number: | 2-4 | ||||||
| Page Range: | pp. 219-251 | ||||||
| DOI: | 10.25596/jalc-2019-219 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Publisher Statement: | Accepted for publication in the Journal of Automata, Languages and Combinatorics. This is the author's version of the following article: Chistikov, Dmitry, Martyugin, Pavel and Shirmohammadi, Mahsa (2019) Synchronizing automata over nested words. Journal of Automata, Languages and Combinatorics, 24 (2-4). pp. 219-251. doi:10.25596/jalc-2019-219.. It has been published in final form at https://doi.org/10.25596/jalc-2019-219. This article may be used for non-commercial purposes only. | ||||||
| Access rights to Published version: | Open Access | ||||||
| Copyright Holders: | © Institut für Informatik · Justus-Liebig-Universität Giessen | ||||||
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