LIPIcs.STACS.2021.52.pdf
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Lower Bounds for Graph-Walking Automata
Authors
Olga Martynova 
,
Alexander Okhotin
-
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38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2021-03-10
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Author Details
- Department of Mathematics and Computer Science, St. Petersburg State University, Russia
Cite AsGet BibTex
Olga Martynova and Alexander Okhotin. Lower Bounds for Graph-Walking Automata. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 52:1-52:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.52
https://doi.org/10.4230/LIPIcs.STACS.2021.52
Abstract
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Formal languages and automata theory
- Theory of computation → Models of computation
Keywords
- Finite automata
- graph-walking automata
- halting
- reversibility
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References
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