Abstract
Let ℂ be the class of real-time nondeterministic one-counter machines whose counters make at mostone reversal. Let ℂ1 (respectively, ℂ2) be the subclass consisting of machines whose only nondeterministic move is in the choice of when to reverse the counter (respectively, when to start using the counter). ℂ1 and ℂ2 are among the simplest known classes of machines for which the universe problem has been shown undecidable. (The universe problem for a class of machines is the problem of deciding if an arbitrary machine in the class accepts all its inputs.) Here, we show that the classes of languages accepted by machines in ℂ1 and ℂ2 are incomparable. Moreover, the union of the language classes is properly contained in the class defined by ℂ. We also, briefly, look at the closure properties of these machines.
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References
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This research was supported in part by NSF Grant MCS78-01736.
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Ibarra, O.H., Rosier, L.E. On restricted one-counter machines. Math. Systems Theory 14, 241–245 (1981). https://doi.org/10.1007/BF01752400
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DOI: https://doi.org/10.1007/BF01752400