Speed-up of Turing machines with one work tape and a two-way input tape
SIAM Journal on Computing
A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
On the power of one-way communication
Journal of the ACM (JACM)
Two-dimensional iterative arrays: characterizations and applications
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
Speedup of determinism by alternation for multidimensional Turing machines
Theoretical Computer Science
Nondeterministic, probabilistic and alternating computations on cellular array models
Theoretical Computer Science
Alternation on cellular automata
Theoretical Computer Science
Invertible linear cellular automata over Zm: algorithmic and dynamical aspects
Journal of Computer and System Sciences
Computations on nondeterministic cellular automata
Information and Computation
Two-dimensional cellular automata recognizer
Theoretical Computer Science - Special issue on Caen '97
Journal of the ACM (JACM)
Algorithms for leader election by cellular automata
Journal of Algorithms
Constructible functions in cellular automata and their applications to hierarchy results
Theoretical Computer Science
Speeding-Up Nondeterministic Single-Tape Off-Line Computations by One Alternation
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The Quest for Small Universal Cellular Automata
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Speeding-up Single-Tape Nondeterministic Computations by Single Alternation, with Separation Results
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Signals for Cellular Automata in Dimension 2 or Higher
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Real-Time Language Recognition by Alternating Cellular Automata
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Real-Time Computation by n-Dimensional Iterative Arrays of Finite-State Machines
IEEE Transactions on Computers
Tape bounds for time-bounded turing machines
Journal of Computer and System Sciences
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We present simulation and separation results between multi-dimensional deterministic and alternating cellular automata (CAs). It is shown that for any integers k≥l≥1, every k-dimensional t(n)-time deterministic CA can be simulated by an l-dimensional O(t(n)^{(k-l+1)/(k-l+2}))-time alternating CA. This result is a dimension reduction theorem and also a time reduction theorem: (i) Every multi-dimensional deterministic CA can be simulated by a one-dimensional alternating CA without increasing time complexity. (ii) Every deterministic computation in a multi-dimensional deterministic CA can be sped up quadratically by alternations when the dimension is fixed. Furthermore, it is shown that there is a language which can be accepted by a one-dimensional alternating CA in t(n) time but not by any multi-dimensional deterministic CA in t(n) time.