Summary
A generalized iterative array model in which the next state of each finite-state computing element may depend on the signs of its location's coordinates and the current state of the computing element at the array origin (“direct central control”) is shown to be no more powerful for on-line time-bounded operation than the standard model of Cole. Applications include a simple iterative array simulation of multihead Turing machines of the same dimension, a simulation without time loss of a further generalized iterative array model with multiple “array heads” which may be shifted locally in the array or reset instantaneously to each other's locations, and simplified versions of several published iterative array algorithms.
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References
Atrubin, A.J.: A one-dimensional real-time iterative multiplier. IEEE Trans. Electronic Computers EC-14, 394–399 (1965)
Beyer, W.T.: Recognition of topological invariants by iterative arrays. Massachusetts Institute of Technology, Cambridge (Mass.), Doctoral Thesis, June 1969
Cole, S.N.: Real-time computation by iterative arrays of finite-state machines. Harvard University, Cambridge (Mass.), Doctoral Thesis, August 1964
Cole, S.N.: Real-time computation by n-dimensional iterative arrays of finite-state machines. IEEE Trans. Computers C-13, 349–365 (1969)
Cole, S.N.: Deterministic pushdown store machines and real-time computation. J. ACM 18, 306–328 (1971)
Fischer, P.C.: Generation of primes by a one-dimensional real-time iterative array. J. ACM 12, 388–394 (1965)
Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Real-time simulation of multihead tape units. J. ACM 19, 590–607 (1972)
Galil, Z.: Real-time algorithms for string-matching and palindrome recognition. Proc. 8th Annual ACM Symposium on Theory of Computing, Hershey (Pa.), pp. 161–173, 1976
Galil, Z., Seiferas, J.I.: Recognizing certain repetitions and reversals within strings. 17th Annual Symposium on Foundations of Computer Science, Houston (Texas), pp. 236–252, 1976
Hamacher, V.C.: Machine complexity versus interconnection complexity in iterative arrays. IEEE Trans. Computers C-20, 321–323 (1971)
Kosaraju, S.R.: Computations on iterative automata. University of Pennsylvania, Philadelphia (Pa.), Doctoral Thesis, August 1969
Kosaraju, S.R.: 1-way stack automata with jumps. J. Computer and System Sciences 9, 164–176 (1974)
Kosaraju, S.R.: Speed of recognition of context-free languages by array automata. SIAM J. Computing 4, 331–340 (1975)
Leong, B.L., Seiferas, J.I.: New real-time simulations of multihead tape units. 9th Annual ACM Symposium on Theory of Computing Boulder (Colorado), 1977
Seiferas, J.I.: Observations on nondeterministic multidimensional iterative arrays. Proc. 6th Annual ACM Symposium on Theory of Computing, Seattle (Wash.), pp. 276–289, 1974
Slisenko, A.O.: Recognition of palindromes by multihead Turing machines. In: Problems in the constructive trend in mathematics, Vol. VI (Proceedings of the Steklov Institute of Mathematics, No. 129) (V.P. Orevkov, N.A. Šanin, eds.), Academy of Sciences of the USSR, pp. 30–202, 1973; English translation by R.H. Silverman, American Mathematical Society, Providence (R.I.), pp.25–208, 1976
Smith, A.R. III: Cellular automata complexity trade-offs. Information and Control 18, 466–482 (1971)
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Seiferas, J.I. Iterative arrays with direct central control. Acta Informatica 8, 177–192 (1977). https://doi.org/10.1007/BF00289248
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DOI: https://doi.org/10.1007/BF00289248