Various Solutions to the Firing Squad Synchronization Problems

Abstract

We present different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes. The nodes are finite state processors that work at unison discrete steps. The networks considered are the line, the ring and the square. For all of these models we have considered one and two-way communication modes and also constrained the quantity of information that adjacent processors can exchange each step. We are given a particular time expressed as a function of the number of nodes of the network, $f(n)$ and present synchronization algorithms in time $n^2$, $n \log n$, $n\sqrt n$, $2^n$. The solutions are presented as {\em signals} that are used as building blocks to compose new solutions for all times expressed by polynomials with nonnegative coefficients.