Abstract
Then-dimensional origin-crossing language,O n, is a language each of whose words describes a walk throughn-dimensional space beginning and ending at the origin. For eachn, O n is real-time recognizable by ann-counter machine but not by any (n — 1)-counter machine. In contrast, for alln, O n is real-time recognizable by a one-tape Turing machine.
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Fischer, M.J., Rosenberg, A.L. Real-time solutions of the origin-crossing problem. Math. Systems Theory 2, 257–263 (1968). https://doi.org/10.1007/BF01694010
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DOI: https://doi.org/10.1007/BF01694010