In a recent paper, Dobronravov et al. (“On the length of shortest strings accepted by two-way finite automata”, DLT 2019) prove that the shortest string in a language recognized by an n-state two-way finite automaton (2DFA) can be at least symbols long, improved to in their latest contribution. The lower bound was obtained using “direction-determinate” 2DFA, which always remember their direction of motion at the last step, and used an alphabet of size In this paper, the method of Dobronravov et al. is extended to a new, more general class: the semi-direction-determinate 2DFA. This yields n-state 2DFA with shortest strings of length Furthermore, the construction is adapted to use a fixed alphabet, resulting in shortest strings of length It is also shown that an n-state semi-direction-determinate 2DFA can be transformed to a one-way NFA with states.

Original languageEnglish
Title of host publicationDescriptional Complexity of Formal Systems - 22nd International Conference, 2020, Proceedings
EditorsGalina Jirásková, Giovanni Pighizzini
PublisherSpringer Nature
Number of pages13
ISBN (Print)9783030625351
Publication statusPublished - 2020
Event22nd International Conference on Descriptional Complexity of Format Systems, DCFS 2020 - Vienna
Duration: 24 Aug 202026 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12442 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Conference on Descriptional Complexity of Format Systems, DCFS 2020

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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