State-Efficient Firing Squad Synchronization Protocols for Communication-Restricted Cellular Automata

An Overview of Recent Solutions to and Lower Bounds for the Firing Synchronization Problem

“…In this paper the authors Umeo, Kamikawa, Nishioka and Akiguchi [20] present a computer study on different solutions to the generalized firing synchronization problem (GFSP). Recall that the GFSP may be described as the original problem with the general on the far left or right of the array at time t = −(k − 1), where k is the number of cells between the general and the nearest end.…”

“…This 5-state solution is a small but partial solution to the original problem, since it has some limitations regarding the length of the array n. Other authors like Settle and Simon [15] and Umeo [26] provided complete solutions to the generalized problem using the same kind of algorithm but with a higher number of states. Settle and Simon provided a solution using only 7 states [15], and Umeo did using 6 states [26]. Unlike this one in both solutions the initiator can be placed in any part of the array.…”

“…Since then his work has been improved in 1999 by Settle to a 9-state solution [16]. In 2010 Umeo, Kamikawa and Nishioka [20] presented a 8-state minimal-time solution which is currently the smallest minimal-time solution to the generalized problem.…”