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RealTime Computation by nDimensional Iterative Arrays of FiniteState Machines
April 1969 (vol. 18 no. 4)
pp. 349365
ASCII Text  x  
S.N. Cole, "RealTime Computation by nDimensional Iterative Arrays of FiniteState Machines," IEEE Transactions on Computers, vol. 18, no. 4, pp. 349365, April, 1969.  
BibTex  x  
@article{ 10.1109/TC.1969.222663, author = {S.N. Cole}, title = {RealTime Computation by nDimensional Iterative Arrays of FiniteState Machines}, journal ={IEEE Transactions on Computers}, volume = {18}, number = {4}, issn = {00189340}, year = {1969}, pages = {349365}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1969.222663}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  RealTime Computation by nDimensional Iterative Arrays of FiniteState Machines IS  4 SN  00189340 SP349 EP365 EPD  349365 A1  S.N. Cole, PY  1969 KW  Acceptor KW  computation KW  computing capability KW  contextfree language KW  iterative array KW  ndimensional KW  palindrome KW  real time. VL  18 JA  IEEE Transactions on Computers ER   
An ndimensional iterative array of finitestate machines is formally introduced as a realtime tape acceptor. The computational characteristics of iterative arrays are illuminated by establishing several results concerning the sets of tapes that they recognize. Intercommunication between machines in an array is characterized by specifying a stencil for the array. The computing capability of the array is preserved even if its stencil is reduced to a simple form in which machines communicate only with their nearest neighbors. An increase of computing speed by a constant factor k is defined by encoding klength blocks of the input tapes, which reduces the lengths of the tapes by 1/k; the time available for computation is correspondingly reduced since the computation must be real time. The computation speed of iterative arrays can be increased by any constant factor k. Two examples of onedimensional arrays are provided. The first accepts the set of palindromes; the second accepts the set of all tapes of the form tt (for any tape t). The latter set of tapes is not a contextfree language; therefore, the sets of tapes accepted by iterative arrays are not all contained in the class of contextfree languages. Conversely, the class of contextfree languages is not contained in the class of sets of tapes accepted by iterative arrays. The sets of tapes accepted by iterative arrays are closed under the operations: union, intersection, and complement; therefore, they form a Boolean algebra. They are not closed under the reflection or concatenationproduct operations.
Index Terms:
Acceptor, computation, computing capability, contextfree language, iterative array, ndimensional, palindrome, real time.
Citation:
S.N. Cole, "RealTime Computation by nDimensional Iterative Arrays of FiniteState Machines," IEEE Transactions on Computers, vol. 18, no. 4, pp. 349365, April 1969, doi:10.1109/TC.1969.222663
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