On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

Sublinearly space bounded iterative arrays

Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio

On Measuring Non-Recursive Trade-Offs

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems

Fast cellular automata with restricted inter-cell communication: computational capacity

A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. 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 iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as {ap│prim} or {a2n│n∈N}[16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite diferent from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Fast cellular automata with restricted inter-cell communication: computational capacity

A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. 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 iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as {ap│prim} or {a2n│n∈N}[16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite diferent from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Fast cellular automata with restricted inter-cell communication: computational capacity

A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. 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 iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as {ap│prim} or {a2n│n∈N}[16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite diferent from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

The Size of One-Way Cellular Automata

International audienceWe investigate the descriptional complexity of basic operations on real-time one-way cellular automata with an unbounded as well well as a fixed number of cells. The size of the automata is measured by their number of states. Most of the bounds shown are tight in the order of magnitude, that is, the sizes resulting from the effective constructions given are optimal with respect to worst case complexity. Conversely, these bounds also show the maximal savings of size that can be achieved when a given minimal real-time OCA is decomposed into smaller ones with respect to a given operation. From this point of view the natural problem of whether a decomposition can algorithmically be solved is studied. It turns out that all decomposition problems considered are algorithmically unsolvable. Therefore, a very restricted cellular model is studied in the second part of the paper, namely, real-time one-way cellular automata with a fixed number of cells. These devices are known to capture the regular languages and, thus, all the problems being undecidable for general one-way cellular automata become decidable. It is shown that these decision problems are $\textsf{NLOGSPACE}$-complete and thus share the attractive computational complexity of deterministic finite automata. Furthermore, the state complexity of basic operations for these devices is studied and upper and lower bounds are given

Cellular automata with limited inter-cell bandwidth

AbstractA 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 {ap∣p prime} or {a2n∣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

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast