Firing squad synchronization problem in reversible cellular automata

Imai, Katsunobu; Morita, Kenichi

doi:10.1016/0304-3975(96)00016-3

Cited by 36 publications

(14 citation statements)

References 6 publications

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“…Kari 2005). As for other information processing ability of RCAs, there is a study on the firing squad synchronization problem on an RCA by Imai and Morita (1996), where a 3n-step solution was given. Self-replication of patterns is also possible in 2D and 3D RCAs (Imai, Hori, and Morita 2002).…”

Section: Discussionmentioning

confidence: 99%

Computation in reversible cellular automata

Morita

2012

International Journal of General Systems

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A reversible cellular automaton (RCA) is a subclass of a CA such that its global function is injective. It is considered as an abstract spatiotemporal model of a reversible physical system. In spite of the strong constraint of reversibility, an RCA has a high ability of information processing. In this survey, we overview the past studies on RCAs, and discuss how computing is performed in them. We can see even very simple RCAs have computation-universality.

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Section: Discussionmentioning

confidence: 99%

Computation in reversible cellular automata

Morita

2012

International Journal of General Systems

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“…When the first a is read, a reversible version of the Firing Squad Synchronization Problem (FSSP) according to the construction given in [12] is started on the fourth track. At time 2(|w| + 2) + n the cells 0, .…”

Section: Theorem 20 Let M Be a Real-time Ia It Is Not Semidecidablementioning

confidence: 99%

Real-time reversible iterative arrays

Kutrib

Malcher

2010

Theoretical Computer Science

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a b s t r a c tIterative arrays are one-dimensional arrays of interconnected interacting finite automata. The cell at the origin is equipped with a one-way read-only input tape. We investigate iterative arrays as acceptors for formal languages. In particular, we consider real-time devices which are reversible on the core of computation, i.e., from initial configuration to the configuration given by the time complexity. This property is called real-time reversibility. It is shown that real-time reversible iterative arrays can simulate restricted variants of stacks and queues. It turns out that real-time reversible iterative arrays are strictly weaker than real-time reversible cellular automata. On the other hand, a nonsemilinear language is accepted. We show that real-time reversibility itself is not even semidecidable, which extends the undecidability for cellular automata and contrasts with the general case, where reversibility is decidable for one-dimensional devices. Moreover, we prove the non-semidecidability of several other properties. Several closure properties are also derived.

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“…Adapting the proof for the real u n is just a matter of adding a finite set of special states to deal with constants. The proof is based on a reversible solution B to the firing squad synchronization problem proposed by K. Imai and K. Morita: in [16], they construct a reversible CA B with a subset of states F (the firing states) such that for any n, there is a periodic configuration c n verifying 7 :…”

Section: A a × A A × A × A · · ·mentioning

confidence: 99%

“…In[16], the main concern is synchronisation of finite segments of cells surrounded by a quiescent state. To extend the property to infinite configurations, it is crucial that "garbage" (which must be conserved to ensure reversibility) do no spread outside the initial segment.…”

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Bulking II: Classifications of cellular automata

Delorme

Mazoyer²,

Ollinger³

et al. 2011

Theoretical Computer Science

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International audienceThis paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc.) providing several formal tools allowing to classify cellular automata

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Firing squad synchronization problem in reversible cellular automata

Cited by 36 publications

References 6 publications

Computation in reversible cellular automata

Computation in reversible cellular automata

Real-time reversible iterative arrays

Bulking II: Classifications of cellular automata

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