Abstract

Given a two-way finite automaton recognizing a non-empty language, consider the length of the shortest string it accepts, and, for each n ≥ 1, let f(n) be the maximum of these lengths over all n-state automata. It is proved that for n-state two-way finite automata, whether deterministic or nondeterministic, this number is at least Ω(8n/5) and less than, with the lower bound reached over an alphabet of size Θ(n). Furthermore, for deterministic automata and for a fixed alphabet of size m ≥ 1, the length of the shortest string is at least (Formula Presented).

Original languageEnglish
Title of host publicationDevelopments in Language Theory - 23rd International Conference, DLT 2019, Proceedings
EditorsPiotrek Hofman, Michał Skrzypczak
PublisherSpringer
Pages88-99
Number of pages12
ISBN (Print)9783030248857
DOIs
Publication statusPublished - 1 Jan 2019
Event23rd International Conference on Developments in Language Theory, DLT 2019 - Warsaw
Duration: 5 Aug 20199 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11647 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Conference on Developments in Language Theory, DLT 2019
CountryPoland
CityWarsaw
Period5/08/199/08/19

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Scopus subject areas

  • Theoretical Computer Science

Cite this

Dobronravov, E., Dobronravov, N., & Okhotin, A. (2019). On the length of shortest strings accepted by two-way finite automata. In P. Hofman, & M. Skrzypczak (Eds.), Developments in Language Theory - 23rd International Conference, DLT 2019, Proceedings (pp. 88-99). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11647 LNCS). Springer. https://doi.org/10.1007/978-3-030-24886-4_6