Abstract
In this paper we consider two-way counter machines, i.e., two-way finite automata with counters whose contents have no effect on transitions except that an attempt to decrement an empty counter will abort the computation. We show that the deterministic machines have an unsolvable emptiness problem, but that their universe problem is solvable because they accept languages whose complements are context free. In the nondeterministic case, we show that these machines are equivalent to two-way nondeterministic logspace Turing machines, and establish an infinite hierarchy based on the number of weak counters. Finally, we disprove two conjectures concerning the nondeterministic machines.
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