On Some Open Problems Concerning the Complexity of Cellular Arrays

We give a brief account of the progress that has been made in the last few years concerning the computational complexity of cellular arrays, and cite a few important open problems that remain unresolved.

[1]  Oscar H. Ibarra,et al.  Characterizations and Computational Complexity of Systolic Trellis Automata , 1984, Theor. Comput. Sci..

[2]  Tao Jiang,et al.  On One-Way Cellular Arrays , 1987, SIAM J. Comput..

[3]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[4]  Lawrence Snyder,et al.  Bounds on minimax edge length for complete binary trees , 1981, STOC '81.

[5]  Hiroshi Umeo,et al.  Deterministic One-Way Simulation of Two-Way Real-Time Cellular Automata and Its Related Problems , 1982, Inf. Process. Lett..

[6]  Arto Salomaa,et al.  Systolic trellis automatat , 1984 .

[7]  S. Rao Kosaraju.  On Some Open Problems in the Theory of Cellular Automata , 1974, IEEE Transactions on Computers.

[8]  Oscar H. Ibarra,et al.  Two-Dimensional Iterative Arrays: Characterizations and Applications , 1988, Theor. Comput. Sci..

[9]  Oscar H. Ibarra,et al.  On the power one-way communication , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[10]  Alvy Ray Smith.  Cellular Automata and Formal Languages , 1970, SWAT.

[11]  Oscar H. Ibarra,et al.  On Iterative and Cellular Tree Arrays , 1989, J. Comput. Syst. Sci..

[12]  Tao Jiang,et al.  Optimal Simulation of Tree Arrays by Linear Arrays , 1989, Inf. Process. Lett..

[13]  Alvy Ray Smith,et al.  Cellular Automata Complexity Trade-Offs , 1971, Inf. Control..

[14]  Azriel Rosenfeld,et al.  Triangle Cellular Automata , 1981, Inf. Control..

[15]  Oscar H. Ibarra,et al.  Efficient Simulations of Simple Models of Parallel Computation by Time-Bounded ATMs and Space-Bounded TMs , 1989, Theor. Comput. Sci..

[16]  Stephen N. Cole.  Real-Time Computation by n-Dimensional Iterative Arrays of Finite-State Machines , 1969, IEEE Trans. Computers.

[17]  Tao Jiang,et al.  Relating the Power of Cellular Arrays to Their Closure Properties , 1988, Theor. Comput. Sci..

[18]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[19]  Alvy Ray Smith,et al.  Real-Time Language Recognition by One-Dimensional Cellular Automata , 1972, J. Comput. Syst. Sci..

[20]  Charles R. Dyer,et al.  One-Way Bounded Cellular Automata , 1980, Inf. Control..

[21]  Oscar H. Ibarra,et al.  Iterative tree arrays with logarithmic depth , 1986 .

[22]  Oscar H. Ibarra,et al.  Designing Systolic Algorithms Using Sequential Machines , 1986, IEEE Transactions on Computers.

[23]  Karel Culik,et al.  On Real Time and Linear Time Cellular Automata , 1984, RAIRO Theor. Informatics Appl..

[24]  Oscar H. Ibarra,et al.  Some results concerning linear iterative (systolic) arrays , 1985, J. Parallel Distributed Comput..

[25]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[26]  Mike Paterson.  Tape Bounds for Time-Bounded Turing Machines , 1972, J. Comput. Syst. Sci..

[27]  Oscar H. Ibarra,et al.  Sequential Machine Characterizations of Trellis and Cellular Automata and Applications , 1985, SIAM J. Comput..