On Cellular Automata with a Finite Number of State Changes

Vollmar, Roland

doi:10.1007/978-3-7091-8596-4_13

Cited by 24 publications

(27 citation statements)

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“…, b i j,1 +...+i j,k . This can be achieved by an obvious In conclusion we remark that the results can also be adapted to cellular automata where the number of proper state changes is bounded [19,20], which answers an open question posed in [21]. Analyzing the proofs of Lemma 13, Lemma 14, and Lemma 15 with respect to the number of state changes shows that the language L(p) is accepted by real-time cellular automata where the number of state changes of each cell is bounded by a constant.…”

Section: Decidability Questionsmentioning

confidence: 94%

“…In [19,20] two-way cellular automata are considered where the number of proper state changes is bounded. Similar as in the present paper the sum of all state changes or the maximal number of the state changes of single cells are bounded.…”

Section: Computational Capacitymentioning

confidence: 99%

“…Whether or not state change bounded devices are strictly weaker than communication bounded ones is an open problem. However, the restrictions introduced in [19,20] have been investigated with respect to communication in cellular automata, and the proof methods used apply also for the devices in question. So, we adapt some of the results shown in connection with state changes in the next theorem.…”

Section: Computational Capacitymentioning

confidence: 99%

“…The former question concerns the amount of communication necessary for a computation. In [19,20] two-way cellular automata are considered where the number of proper state changes is bounded. There are strong relations to inter-cell communication.…”

Section: Introductionmentioning

confidence: 99%

“…Then, in Section 3 some computational capacity aspects are investigated, where an infinite strict hierarchy depending on the bound on the total number of communications during an computation is shown. Since the proof methods used in connection with the number of state changes in [19,20] apply also for the devices in question we adapt and summarize some of the known results.…”

Section: Introductionmentioning

confidence: 99%

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Cellular Automata with Sparse Communication

Kutrib

Malcher

2009

Implementation and Application of Automata

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Abstract. We investigate cellular automata whose internal inter-cell communication is bounded. The communication is quantitatively measured by the number of uses of the links between cells. Bounds on the sum of all communications of a computation as well as bounds on the maximal number of communications that may appear between each two cells are considered. It is shown that even the weakest non-trivial device in question, that is, one-way cellular automata where each two neighboring cells may communicate constantly often only, accept rather complicated languages. We investigate the computational capacity of the devices in question and prove an infinite strict hierarchy depending on the bound on the total number of communications during a computation. Despite their sparse communication even for the weakest devices, by reduction of Hilbert's tenth problem undecidability of several problems is derived. Finally, the question whether a given real-time one-way cellular automaton belongs to the weakest class is shown to be undecidable. This result can be adapted to answer an open question posed in [Vollmar, R.: Zur Zustandsänderungskom-plexität von Zellularautomaten. In: Beiträge zur Theorie der Polyautomaten-zweite Folge, Braunschweig (1982) 139-151 (in German)].

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Section: Decidability Questionsmentioning

confidence: 94%

Section: Computational Capacitymentioning

confidence: 99%

Section: Computational Capacitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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