Parallel parsing on a one-way array of finite-state machines
IEEE Transactions on Computers
Two-dimensional iterative arrays: characterizations and applications
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
On real time one-way cellular array
Theoretical Computer Science
Generation of Primes by a One-Dimensional Real-Time Iterative Array
Journal of the ACM (JACM)
Parallel Computing - Special issue on cellular automata: from modeling to applications
Fundamenta Informaticae - Special issue on cellular automata
Iterative Arrays with Small Time Bounds
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Linear Time Language Recognition on Cellular Automata with Restricted Communication
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On Time-Constructible Functions in One-Dimensional Cellular Automata
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Iterative Arrays with a Wee Bit Alternation
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Real-time generation of primes by a 1-bit-communication cellular automaton
Fundamenta Informaticae - Special issue on cellular automata
Real-Time Computation by n-Dimensional Iterative Arrays of Finite-State Machines
IEEE Transactions on Computers
Real-time language recognition by one-dimensional cellular automata
Journal of Computer and System Sciences
Hi-index | 5.23 |
A d-dimensional cellular automaton is a d-dimensional grid of interconnected interacting finite automata. There are models with parallel and sequential input modes. In the latter case, the distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as an iterative array. In this paper, d-dimensional iterative arrays and one-dimensional cellular automata are investigated which operate in real and linear time and whose inter-cell communication bandwidth is restricted to some constant number of different messages independent of the number of states. It is known that even one-dimensional two-message iterative arrays accept rather complicated languages such as {a^p|p prime} or {a^2^^^n|n@?N} (H. Umeo, N. Kamikawa, Real-time generation of primes by a 1-bit-communication cellular automaton, Fund. Inform. 58 (2003) 421-435). Here, the computational capacity of d-dimensional iterative arrays with restricted communication is investigated and an infinite two-dimensional hierarchy with respect to dimensions and messages is shown. Furthermore, the computational capacity of the one-dimensional devices in question is compared with the power of two-way and one-way cellular automata with restricted communication. It turns out that the relations between iterative arrays and cellular automata are quite different from the relations in the unrestricted case. Additionally, an infinite strict message hierarchy for real-time two-way cellular automata is obtained as well as a very dense time hierarchy for k-message two-way cellular automata. Finally, the closure properties of one-dimensional iterative arrays with restricted communication are investigated and differences to the unrestricted case are shown as well.