A Spatio-temporal Algorithmic Point of View on Firing Squad Synchronisation Problem

Maignan, Luidnel; Yunès, Jean-Baptiste

doi:10.1007/978-3-642-33350-7_11

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…We already gave a solution to the 1D-FSSP using fields in a previous paper (see [15]), so we will only sketch its description to help the reader comparing the 1D and 2D cases.…”

Section: Distance Fields Halving and Recursionmentioning

confidence: 98%

Moore and Von Neumann Neighborhood N-Dimensional Generalized Firing Squad Solutions Using Fields

Maignan

Yunès²

2013

2013 First International Symposium on Computing and Networking

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“…We already gave a solution to the 1D-FSSP using fields in a previous paper (see [15]), so we will only sketch its description to help the reader comparing the 1D and 2D cases.…”

Section: Distance Fields Halving and Recursionmentioning

confidence: 98%

Moore and Von Neumann Neighborhood N-Dimensional Generalized Firing Squad Solutions Using Fields

Maignan

Yunès²

2013

2013 First International Symposium on Computing and Networking

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“…In 2012, Maignan and Yunes proposed the methodology of cellular fields to described formally the high-level implementation of a CA, and also formally the generation of the "low-level" transition table. One of the expected benefits was to have an infinite CA cleanly modularized into many cellular fields with clear semantical proof of correctness together with a correctness-preserving reduction procedure into a finite state CA [5] using a particular kind of cellular field, "reductions". This is very similar to what happen in usual computer programming where one writes in a high-level language then transform the code into assembly using a semantic-preserving transformation, i.e.…”

Section: Context Of the Initial Motivationsmentioning

confidence: 99%

Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation

Nguyen¹,

Maignan²

2020

Preprint

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In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n − 2 for n cells) and, up to current knowledge, also in states (6 states). While only one such solution was proposed by Mazoyer since 1987, 718 new solutions have been generated by Clergue, Verel and Formenti in 2018 with a cluster of machines. We show here that, starting from existing solutions, it is possible to generate millions of such solutions using local simulations using a single common personal computer.

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“…This problem have been studied from the 1960's [9,17,20], with a wide range of construction [3,15,16] and is still active nowadays [10,11,12,13,19,21]. In [15], a six-state minimal time solution is given.…”

Section: Introductionmentioning

confidence: 99%

Abstract geometrical computation 4: Small Turing universal signal machines

Durand-Lose

2011

Theoretical Computer Science

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Abstract geometrical computation 4: small Turing universal signal machinesJérôme Durand-Lose To cite this version:Jérôme Durand-Lose. Abstract geometrical computation 4: small Turing universal signal machines. Theoretical Computer Science, Elsevier, 2011, 412, pp. AbstractThis article provides several very small signal machines able to perform any computation -in the classical understanding-generated from Turing machines, cellular automata and cyclic tag systems. A halting universal signal machine with 13 metasignals and 21 collision rules is presented (resp. 15 and 24 for a robust version). If infinitely many signals are allowed to be present in the initial configuration, 5 metasignals and 7 collision rules are enough to achieve non-halting weak universality (resp. 6 and 9 for a robust version).

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A Spatio-temporal Algorithmic Point of View on Firing Squad Synchronisation Problem

Cited by 10 publications

References 15 publications

Moore and Von Neumann Neighborhood N-Dimensional Generalized Firing Squad Solutions Using Fields

Moore and Von Neumann Neighborhood N-Dimensional Generalized Firing Squad Solutions Using Fields

Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation

Abstract geometrical computation 4: Small Turing universal signal machines

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