We show the undecidability of the universe problem for two restricted classes of nondeterministic one-counter machines. These classes are among the simplest known for which the universe problem can be shown unsolvable.
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This research was supported by National Science Foundation Grants DCR75-17090 and MCS78-01736.
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Ibarra, O.H. Restricted one-counter machines with undecidable universe problems. Math. Systems Theory 13, 181–186 (1979). https://doi.org/10.1007/BF01744294