2026-07-24T06:34:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13697 2024-03-06T10:52:41Z ddc:004 open_access

Lower Bounds for Graph-Walking Automata Martynova, Olga Okhotin, Alexander Finite automata graph-walking automata halting reversibility Graph-walking automata (GWA) traverse graphs by moving between the nodes following the edges, using a finite-state control to decide where to go next. It is known that every GWA can be transformed to a GWA that halts on every input, to a GWA returning to the initial node in order to accept, as well as to a reversible GWA. This paper establishes lower bounds on the state blow-up of these transformations: it is shown that making an n-state GWA traversing k-ary graphs return to the initial node requires at least 2(n-1)(k-3) states in the worst case; the same lower bound holds for the transformation to halting automata. Automata satisfying both properties at once must have at least 4(n-1)(k-3) states. A reversible automaton must have at least 4(n-1)(k-3)-1 states. These bounds are asymptotically tight to the upper bounds proved using the methods from the literature. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Olga Martynova and Alexander Okhotin 2021 Is Part Of LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2021.52 urn:nbn:de:0030-drops-136974 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.52 eng https://creativecommons.org/licenses/by/4.0/legalcode