Parallel parsing on a one-way array of finite-state machines
IEEE Transactions on Computers
Generation of Primes by a One-Dimensional Real-Time Iterative Array
Journal of the ACM (JACM)
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
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
Cellular Automata with Sparse Communication
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
On One-way One-bit O (One)-message Cellular Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
Cellular automata with sparse communication
Theoretical Computer Science
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Iterative arrays (IAs) are one-dimensional arrays of interconnected interacting finite automata with sequential input mode. We investigate IAs which work in real time and whose inter-cell communication is bounded by some constant number of bits not depending on the number of states. It is known [13] that such IAs can recognize rather complicated unary languages with a minimum amount of communication, namely one-bit communication, in real time. Some examples are the languages $\{a^{2^n} \mid n \ge 1\}$, $\{a^{n^2} \mid n \ge 1\}$, and {ap |p is prime}. Here, we consider non-unary languages and it turns out that the non-unary case is quite different. We present several real-time constructions for certain non-unary languages. For example, the languages {anbn |n ≥1}, {an(bn)m |n,m ≥1}, and {anbamb(ba)n .m |n,m ≥1} are recognized in real time by 1-bit IAs. Moreover, it is shown that real-time 1-bit IAs can, in some sense, add and multiply integer numbers. Furthermore, closure properties and decidability questions of communication restricted IAs are investigated. Due to the constructions provided, non-closure results as well as undecidability results can be shown. It turns out that emptiness is still undecidable for 1-bit IAs despite their restricted communication. Thus, also the questions of finiteness, infiniteness, inclusion, and equivalence are undecidable.