Low complexity classes of multidimensional cellular automata

In this paper, multidimensional cellular automaton are considered. We investigate the hierarchy designed by the low complexity classes when the dimensionality is increased. Whether this hierarchy is strict, is an open problem. However, we compare different variants and study their closure properties. We present also a correspondence between a main variant of multidimensional real-time cellular automata and one-way multihead alternating finite automata.

[1]  K. N. King,et al.  Alternating Multihead Finite Automata , 1988, Theor. Comput. Sci..

[2]  Christian Choffrut,et al.  On real-time cellular automata and trellis automata , 2004, Acta Informatica.

[3]  J. Mazoyer,et al.  Cellular Automata as Languages Recognizers , 1999 .

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

[5]  Oscar H. Ibarra,et al.  Parallel Parsing on a One-Way Array of Finite-State Machines , 1987, IEEE Transactions on Computers.

[6]  Véronique Terrier.  Characterization of real time iterative array by alternating device , 2003, Theor. Comput. Sci..

[7]  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..

[8]  Oscar H. Ibarra,et al.  On the Power of One-Way Communication , 1986, FOCS.

[9]  Leslie M. Goldschlager,et al.  A universal interconnection pattern for parallel computers , 1982, JACM.

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

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

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

[13]  Patrick C. Fischer,et al.  Generation of Primes by a One-Dimensional Real-Time Iterative Array , 1965, JACM.

[14]  Karel Culik.  Variations of the Firing Squad Problem and Applications , 1989, Inf. Process. Lett..

[15]  Véronique Terrier,et al.  On Real Time One-Way Cellular Array , 1995, Theor. Comput. Sci..

[16]  M. Delorme,et al.  Cellular automata : a parallel model , 1999 .

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

[18]  Holger Petersen,et al.  Alternation in Simple Devices , 1995, ICALP.