A generalized firing squad problem

R-70-31 A Generalized Firing Squad Problem

New Bounds for the Firing Squad Problem on a Ring

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 sh...

Firing Squad Synchronization Problem in Reversible Cellular Automata

We studied the Firing Squad Synchronization Problem (FSSP) on reversible (i.e., backward deterministic) cellular automata (RCA). First we proved that, in the case of RCA, there is no solution under the usual condition for FSSP where the firing state is only one. So we defined a little weaker condition suitable for RCA in which finite number of firing states are allowed. We showed that Minsky’s ...

On Optimal Solutions to the Firing Squad Synchronization Problem

The one-dimensional firing squad synchronization problem (FSSP) is to construct a generic automaton of a one dimensional cellular network made of a segment of n identical machines so that, whatever the length n of the segment is, 1. if, at the starting time (t = 1 in the following), all finite automata of the cellular network (called cells) are in a quiescent state L and no meaningful piece of ...

Bandwidth of Firing Squad Algorithms

The Firing Squad Synchronization Problem (FSSP) is one of the best-studied problems for Cellular Automata (CA) and is part of many more sophisticated algorithms. Solutions for it such as the one from Mazoyer or Gerken use travelling signals, a basic technique of CA algorithms. Hence in addition to their importance, they represent typical CA algorithms. Beside the interest in their bandwidth fol...