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Seven-state solutions to the firing squad synchronization problem

J.B. Yunès
1994 Theoretical Computer Science  
., Seven-state solutions to the Firing Squad Synchronization Problem, Theoretical Computer Science 127 (1994) 313-332.  ...  We show that seven states are enough to implement Minsky-like solutions to the Firing Squad Synchronization Problem in a linear network of n finite state cellular automata with null transmission delay.  ...  Myhill in 1957, the Firing Squad Synchronization Problem (FSSP) can be expressed as follows: Given a firing squad and knowing that any order given by a general located at one of the two ends needs n units  ... 
doi:10.1016/0304-3975(94)90045-0 fatcat:7p2yg54gt5dttnw67a63k6j57q

An Investigation into Transition Rule Sets for Optimum-time Firing Squad Synchronization Algorithms on One-dimensional Cellular Automata

Hiroshi UMEO, Masaya HISAOKA, Takashi SOGABE
2002 Interdisciplinary Information Sciences  
The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed.  ...  In the present paper, we describe a computer-assisted investigation into state transition tables for which optimum-time synchronization algorithms have been designed.  ...  Firing Squad Synchronization Problem Definition of the Firing Squad Synchronization Problem The firing squad synchronization problem is formalized in terms of the model of cellular automata.  ... 
doi:10.4036/iis.2002.207 fatcat:674p5hgtanb4zds372nzeycb3i

An 8-state minimal time solution to the firing squad synchronization problem

Robert Balzer
1967 Information and Control  
ACKNOWLEDGMENT I am indebted to Dr. Allen Newell for his suggestions and guidance. RECEIVED: February 28, 1966  ...  These seven states and the terminal firing state (F) represent all the states necessary for a minimal time solution to the Firing Squad Synchronization Problem.  ...  does not constitute a solution to the Firing Squad Synchronization Problem.  ... 
doi:10.1016/s0019-9958(67)90032-0 fatcat:r7seiniahfdnrnicfvpfefyqpi

The Firing Squad Synchronization Problems for Number Patterns on a Seven-Segment Display and Segment Arrays

Kazuya YAMASHITA, Mitsuru SAKAI, Sadaki HIROSE, Yasuaki NISHITANI
2010 IEICE transactions on information and systems  
The Firing Squad Synchronization Problem (FSSP), one of the most well-known problems related to cellular automata, was originally proposed by Myhill in 1957 and became famous through the work of Moore  ...  The first solution to this problem was given by Minsky and McCarthy [2] and a minimal time solution was given by Goto [3] .  ...  Acknowledgments The authors are grateful to Mr. Takemasa and Mr. Asai (for-  ... 
doi:10.1587/transinf.e93.d.3276 fatcat:khd4ib6uzzbrvpurvwg7dk6dim

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

Michael J. Dinneen, Yun-Bum Kim, Radu Nicolescu
2009 Electronic Proceedings in Theoretical Computer Science  
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.  ...  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  ...  Acknowledgements The authors wish to thank John Morris and the three anonymous reviewers for detailed comments and feedback that helped us improve the paper.  ... 
doi:10.4204/eptcs.11.7 fatcat:5qt5pu736vegzfn5ecsxb5wsv4

The firing squad synchronization problem with sub-generals

Kazuya Yamashita, Yasuaki Nishitani, Sadaki Hirose, Satoshi Okawa, Nobuyasu Osato
2014 Information Processing Letters  
The Firing Squad Synchronization Problem (FSSP), one of the most well-known problems related to cellular automata, was originally proposed by Myhill in 1957 and became famous through the work of Moore.  ...  In this paper, we introduce a new state called the sub-general to the original problem and propose the FSSP with sub-generals.  ...  Acknowledgements The authors would like to thank the editor and the reviewers who gave us valuable advice and suggestions.  ... 
doi:10.1016/j.ipl.2013.08.003 fatcat:lk2x23jdkzagjes35vhy2iprqe

An efficient solution of the firing mob problem

Karel Culik, Simant Dube
1991 Theoretical Computer Science  
An efficient solution of the firing mob problem, which is the generalization of the well-known "firing squad synchronization" problem to finite bounded-degree networks, is presented.  ...  All rights reserved An eficient solution of the firing mob problem 65  ...  An overview of the firing squad synchronization problem is given in [9] . Here we present an efficient solution of the firing mob problem for general networks.  ... 
doi:10.1016/0304-3975(91)90267-6 fatcat:zkcu4bidxjfejfhxus5m3h7gj4

Synchronization in Quantum-dot Cellular Automata Circuits and Systems

Orestis Liolis, Vassilios A. Mardiris, Georgios Ch. Sirakoulis, Ioannis G. Karafyllidis
2020 IEEE Open Journal of Nanotechnology  
well-known from computer science, Firing Squad Synchronization Problem (FSSP).  ...  Among the numerous FSSP's algorithmic solutions in literature, the Mazoyer algorithm has proven to be the most efficient one.  ...  FIRING SQUAD SYNCHRONIZATION PROBLEM Firing Squad Synchronization (FSS) problem, initially introduced by Myhill (1957) and then solved in the early sixties by Moore [16] , describes a random length  ... 
doi:10.1109/ojnano.2020.3041399 fatcat:fy6aiuvhifgldolk4mxpmbbske

An Iterated Local Search to find many solutions of the 6-states Firing Squad Synchronization Problem

Manuel Clergue, Sébastien Verel, Enrico Formenti
2018 Applied Soft Computing  
This paper proposes an optimization approach for solving a classical problem in cellular automata theory: the 6-states Firing Squad Synchronization Problem (FSSP).  ...  To this purpose, we introduce an original optimization function which quantifies the quality of solutions according only to the main goal of the problem without taking into account any side information  ...  Firing Squad Synchronization Problem The Firing Squad Synchronization Problem (FSSP) was first proposed by Myhill in 1957 and published by Moore in 1964 [4] .  ... 
doi:10.1016/j.asoc.2018.01.026 fatcat:btm2ps32sjhcfb3tz5doai6bre

Page 3135 of Mathematical Reviews Vol. 58, Issue 4 [page]

1979 Mathematical Reviews  
The modified firing squad synchronization problem, in the sense of the present paper, is the following: In a chain of n automata, where each is directly connected with its two neighbours, k au- tomata  ...  The prob- lem is to specify the structure of the automata such that, indepen- dently of the number of automata and generals, all members enter thefirestate at the same time.  ... 

Page 1759 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
(F-PARIS6-BP; Paris) Seven-state solutions to the firing squad synchronization problem. (English summary) Theoret. Comput. Sci. 127 (1994), no. 2, 313-332.  ...  A solution to the (linear cellular automaton) firing squad synchro- nization problem with six states is due to J. Mazoyer [Theoret. Comput. Sci. 50 (1987), no. 2, 183-238; MR 89f:68026].  ... 

A six-state minimal time solution to the firing squad synchronization problem

Jacques Mazoyer
1987 Theoretical Computer Science  
From Balzer's work (1967) , we know that the firing squad synchronization problem has a minimal-time solution with eight states. We show that such a solution exists with only six states.  ...  Our method is somewhat different from all previous ones: the initial line is iteratively divided in two inequal parts so that each new right part can be treated as the homothetical image of a shorter initial  ...  We now prove that the automaton ecti kS . are indicated in Fig. 15 ) is indeed a minimal time solution of the firing squad synchronization problem.  ... 
doi:10.1016/0304-3975(87)90124-1 fatcat:5lrnotub2jfvbk6isxw3zynooy

Recent Developments in Firing Squad Synchronization Algorithms: Smaller Solutions

Hiroshi Umeo
2012 2012 Third International Conference on Networking and Computing  
The synchronization in cellular automata has been known as the firing squad synchronization problem (FSSP).  ...  to the FSSP.  ...  There exist 4-state partial solutions to the firing squad synchronization problem for rings and arrays.  ... 
doi:10.1109/icnc.2012.72 dblp:conf/ic-nc/Umeo12 fatcat:fwxtmemrpvaprddrxzu2hf74gm

Smaller solutions for the firing squad

Amber Settle, Janos Simon
2002 Theoretical Computer Science  
In this paper we improve the bounds on the complexity of solutions to the¯ring squad problem, also known as the¯ring synchronization problem.  ...  In our work we improve the construction for the best known minimal-time solution to the generalized problem by reducing the number of states needed and give non-minimaltime solutions to the original and  ...  In Section 4.1 we present the six-state solution to the original problem, and in Section 4.4 we give the seven-state solution to the generalized problem.  ... 
doi:10.1016/s0304-3975(01)00191-8 fatcat:ar7l6iempfeg3ir5ixhfus5tfm

A universal cellular automaton in quasi-linear time and its S—m—n form

Bruno Martin
1994 Theoretical Computer Science  
This allows us to apply well-known results of the general theory of computation to cellular automata and might give a practical framework for studying the structural complexity of cellular automata computations  ...  The simulation is based on a novel programming language (the brick language), which simplifies the recursive specifications of transition functions.  ...  Firing squad synchronization Thefiring squad synchronization problem is due to Myhill (1957 Each soldier may be represented by a cell of a cellular automaton.  ... 
doi:10.1016/0304-3975(92)00076-4 fatcat:m7t57xxt7ngv7gauqx2loetmhq
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