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On the Size Complexity of Two-Way Finite Automata with Drop-Once Pebbles

Authors Georgy Kipriyanov , Alexander Okhotin

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LIPIcs.MFCS.2026.68.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Models of computation
Keywords
  • Finite automata
  • two-way automata
  • pebble automata
  • determinization

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Abstract

A two-way finite automaton with drop-once pebbles (O. Martynova, A. Okhotin, "A time to cast away stones: On a family of pebble automata", IJFCS, 37 (2026)) may drop its pebbles at any squares of the tape, but a pebble once dropped cannot be moved anymore. In this paper, it is proved that transforming an n-state deterministic automaton with k drop-once pebbles to a standard two-way deterministic finite automaton (2DFA) requires Θ(n^{k+1}) states in the worst case. For nondeterministic two-way automata with one drop-once pebble, it is proved that transforming them to a 2DFA requires at least 2^{n/3-o(n)} states, transforming to a two-way nondeterministic automaton (2NFA) takes at least 2^{n/6-o(n)} states, and, finally, determinizing them to a deterministic two-way automaton with one drop-once pebble requires at least 2^{n/6-o(n)} states.

Cite As Get BibTex

Georgy Kipriyanov and Alexander Okhotin. On the Size Complexity of Two-Way Finite Automata with Drop-Once Pebbles. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 68:1-68:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.68

Author Details

Georgy Kipriyanov
  • Department of Mathematics and Computer Science, Saint Petersburg State University, Russia
Alexander Okhotin
  • Department of Mathematics and Computer Science, Saint Petersburg State University, Russia

Funding

This work was supported by the Russian Science Foundation, project 23-11-00133.

References

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