A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
Variations of the firing squad problem and applications
Information Processing Letters
Faster computation on directed networks of automata
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
Computing with snakes in directed networks of automata
Journal of Algorithms
Smaller solutions for the firing squad
Theoretical Computer Science
New bounds for the distributed firing synchronization problem
New bounds for the distributed firing synchronization problem
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Fundamenta Informaticae - Machines, Computations and Universality, Part I
A smallest five-state solution to the firing squad synchronization problem
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
On the complexity of the “most general” firing squad synchronization problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On formulations of firing squad synchronization problems
UC'05 Proceedings of the 4th international conference on Unconventional Computation
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
An adaptive algorithm for p system synchronization
CMC'11 Proceedings of the 12th international conference on Membrane Computing
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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In this paper we improve the upper and lower bounds on the complexity of solutions to the firing synchronization problem on a ring. In this variant of the firing synchronization problem the goal is to synchronize a ring of identical finite automata. Initially, all automata are in the same state except for one automaton that is designated as the initiator for the synchronization. The goal is to define the set of states and the transition function for the automata so that all machines enter a special fire state for the first time and simultaneously during the final round of the computation. In our work we present two solutions to the ring firing synchronization problem, an 8-state minimal-time solution and a 6-state non-minimal-time solution. Both solutions use fewer states than the previous best-known minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We show that there is no 3-state solution and no 4-state, symmetric, minimal-time solution for the ring.