Consider the emptiness problem for deterministic two-way finite-state automata that are augmented by a bounded-reversal counter and the equivalence problem for deterministic two-way finite-state transducers. The first problem was posed by Ibarra while the second problem restricted to the case that accepting configurations are also halting configurations was posed by Ehrich and Yau. Recently the first problem restricted to devices that accept only bounded languages as well as the restricted version of the second problem have been shown decidable. Here these two problems are shown decidable also in their general form.
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