Recent Developments in Constructing Square Synchronizers

Umeo, Hiroshi; Kubo, Kazuya

doi:10.1007/978-3-642-33350-7_18

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…However g-SQ has not been studied widely. Umeo and Kubo pointed out that at present we do not know whether g-SQ has minimal-time solutions or not ( [25]). The present author derived a formula for the minimum firing time of a configuration C R (w, w, (r, s)) of g-SQ ( [10]).…”

Section: Variations Of Fssp For Rectangles and Squaresmentioning

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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Section: Variations Of Fssp For Rectangles and Squaresmentioning

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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“…For many of these variations minimal-time solutions are known. For surveys on these results we refer readers to [4,5,15,17,21,28,29].…”

Section: The Problem and Its Historymentioning

confidence: 99%

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

Kobayashi¹

2019

Preprint

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“…In the case of a Rectangle of m × n cells, m = n, in [Shi74] the author gave the lower bound for a solution in time n + m + max (m, n) − 2 along with a matching time algorithm. For this case too there is an active research: in [UKT13] a new algorithm has been given which has some nice properties, like the easiness in the verification of its correctness and the fact that it can be extended to a solution for generalized FSSP, where the general is at an arbitrary position in the array (for this feature see also [UK12]). Another peculiarity is that it is isotropic with respect to the shape of a given rectangle array, that is there is no need to control the FSSP algorithm for longer-than-wide and wider-than-long input rectangles.…”

Section: Two and Higher Dimensionsmentioning

confidence: 99%

“…It should be noted that many of the optimum time solutions proposed for the two-dimensional case, are derived from well-known solutions for the onedimensional case, for example those in [UK12,GLP07], embed the synchronization algorithms given by Mazoyer, the former resembles the one of [Maz87] using only 6-states, and the latter, given for 1-bit communication channels, combines that in [Maz96] and the classical of [Shi74].…”

Section: Two and Higher Dimensionsmentioning

confidence: 99%