On Formulations of Firing Squad Synchronization Problems

Kobayashi, Kojiro; Goldstein, Darin

doi:10.1007/11560319_15

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…The six variations considered in this paper are not widely studied. As far as the author knows, papers [7,11,13,22,26] before 1970s and [4,14,16] after 2000s are all the papers on these problems ( [25] considers different but similar variations). However these variations deserve much more interests by researchers.…”

Section: Discussionmentioning

confidence: 99%

“…The traditional model is simple and is suited to present FSSP as an interesting problem in automata theory, and the boundary-sensitive model is suited to the theoretical study of minimal-time solutions. For more details on the boundary-sensitive model, see [15,16].…”

Section: Basic Notions and Notationsmentioning

confidence: 99%

“…by(16). However this upper bound is true only for configurations C such that the value T defined by (15) is the value mft g-kPATH (C).…”

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confidence: 99%

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Minimum firing times of firing squad synchronization problems for paths in grid spaces

Kobayashi¹

2019

Preprint

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Section: Discussionmentioning

confidence: 99%

Section: Basic Notions and Notationsmentioning

confidence: 99%

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Minimum firing times of firing squad synchronization problems for paths in grid spaces

Kobayashi¹

2019

Preprint

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“…For these variations we cannot escape from dealing with the inessential irregularity in the traditional model mentioned above. (See also [11] for the comparison of the two models. )…”

Section: Notions Notations and Technical Preliminariesmentioning

confidence: 99%

Nonexistence of minimal-time solutions for some variations of the firing squad synchronization problem having simple geometric configurations

Kobayashi

2019

Preprint

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We prove nonexistence of minimal-time solutions for three variations of the firing squad synchronization problem (FSSP, for short). Configurations of these variations are paths in the two-dimensional grid space having simple geometric shapes. In the first variation a configuration is an L-shaped path such that the ratio of the length of horizontal line to that of the vertical line is fixed. The general may be at any position. In the second and the third variations a configuration is a rectangular wall such that the ratio of the length of the two horizontal walls to that of the two vertical walls is fixed. The general is at the left down corner in the second variation and may be at any position in the third variation. We use the idea used in the proof of Yamashita et al's recent similar result for variations of FSSP with sub-generals.

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“…The Firing Squad Synchronization Problem (FSSP) [5,6,9,12,14,15] is one of the best studied problems for cellular automata. The problem involves finding a cellular automaton, such that, after a command is given, all the cells, after some finite time, enter a designated firing state simultaneously and for the first time.…”

Section: Introductionmentioning

confidence: 99%

New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

Dinneen

Kim

Nicolescu

2009

Electron. Proc. Theor. Comput. Sci.

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We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast solution is based on a novel proposal, which dynamically extends P systems with mobile channels. The second solution is substantially longer, but is solely based on classical rules and static channels. In contrast to the previous solutions, which work for tree-based P systems, our solutions synchronize to any subset of the underlying digraph; and do not require membrane polarizations or conditional rules, but require states, as typically used in hyperdag and neural P systems

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On Formulations of Firing Squad Synchronization Problems

Cited by 6 publications

References 14 publications

Minimum firing times of firing squad synchronization problems for paths in grid spaces

Minimum firing times of firing squad synchronization problems for paths in grid spaces

Nonexistence of minimal-time solutions for some variations of the firing squad synchronization problem having simple geometric configurations

New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

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