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.
Similar content being viewed by others
References
P. C. Fischer, A. R. Meyer andA. L. Rosenberg, Counter machines and counter languages,Math Systems Theory 2 (1968), 265–283.
J. Hartmanis andR. E. Stearns, On the computational complexity of algorithms.Trans. Amer. Math. Soc. 117 (1965), 285–306.
R. Laing, Realization and complexity of commutative events,Univ. of Mich. Tech. Report 03105-48-T, 1967.
A. L. Rosenberg, Real-time definable languages,J. Assoc. Comp. Mach. 14 (1967), 645–662.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01694010