New Bounds for the Firing Squad Problem on a Ring
نویسندگان
چکیده
We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimaltime solution. Both solutions use fewer states than the previous bestknown 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.
منابع مشابه
On Formulations of Firing Squad Synchronization Problems
We propose a novel formulation of the firing squad synchronization problem. In this formulation we may use more than one general state and the general state to be used is determined by the boundary condition of the general. We show that the usual formulation and the new formulation yield different minimum firing times for some variations of the problem. Our results suggest that the new formulat...
متن کاملSmaller solutions for the firing squad
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 the ̄ring synchronization problem we consider a one-dimensional array of n identical ̄nite automata. Initially all automata are in the same state except for one automaton designated as the initiator for the synchronization. Our results hold for the origi...
متن کاملAn intrinsically non minimal-time Minsky-like 6-states solution to the Firing Squad synchronization problem
Here is presented a 6-states non minimal-time solution which is intrinsically Minsky-like and solves the three following problems: unrestricted version on a line, with one initiator at each end of a line and the problem on a ring. We also give a complete proof of correctness of our solution, which was never done in a publication for Minsky’s solutions. 1991 Mathematics Subject Classification. 6...
متن کاملAbout 4-States Solutions to the Firing Squad Synchronization Problem
We present some elements of a new family of time-optimal solutions to a less restrictive firing squad synchronization problem. These solutions are all built on top of some elementary algebraic cellular automata. Thus, this gives a very new insight on the problem and a more general way of computing on cellular automata.
متن کاملState-efficient Time-optimum Synchronization Protocols for Two-dimensional Arrays -A Survey-
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 give a survey on recent developments in firing squad synchronization algorithms for synchronizing large-scale two-dimensional cellular automata. Several new algorithms and their stateefficient implementatio...
متن کامل