Nondeterminism Is Essential in Small 2FAs with Few Reversals
On every n-long input, every two-way finite automaton (2fa) can reverse its head O(n) times before halting. A 2FA with few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2 h ) states on every deterministic 2FA with few reversals, but only h states on a nondeterministic 2FA with few reversals.
KeywordsHard Instance Generic String Logarithmic Space Tight Lower Bound Input Head
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