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arXiv · 2602.24279

A quadratic lower bound for 2DFAs against one-way liveness

Kehinde Adeogun·Christos Kapoutsis
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Abstract

We show that every two-way deterministic finite automaton (2DFA) that solves one-way liveness on height h has Omega(h^2) states. This implies a quadratic lower bound for converting one-way nondeterministic finite automata to 2DFAs, which asymptotically matches Chrobak's well-known lower bound for this conversion on unary languages. In contrast to Chrobak's simple proof, which relies on a 2DFA's inability to differentiate between any two sufficiently distant locations in a unary input, our argument can be applied to inputs over any alphabet and is structured around a main lemma that is general enough to potentially be reused elsewhere.

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Kehinde Adeogun, Christos Kapoutsis. 2026-02-27. A quadratic lower bound for 2DFAs against one-way liveness. https://arxiv.org/abs/2602.24279

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