# A faster algorithm for the Birthday Song Singers Synchronization Problem (FSSP) in one-dimensional CA with multiple speeds

Worsch, Thomas 1
1 Karlsruher Institut für Technologie (KIT)

## Abstract:

In cellular automata with multiple speeds for each cell i there is a positive integer p$_{i}$ such that this cell updates its state still periodically but only at times which are a multiple of p$_{i}$. Additionally there is a finite upper bound on all p$_{i}$. Manzoni and Umeo have described an algorithm for these (one-dimensional) cellular automata which solves the Firing Squad Synchronization Problem. This algorithm needs linear time (in the number of cells to be synchronized) but for many problem instances it is slower than the optimum time by some positive constant factor. In the present paper we derive lower bounds on possible synchronization times and describe an algorithm which is never slower and in some cases faster than the one by Manzoni and Umeo and which is close to a lower bound (up to a constant summand) in more cases.

 Zugehörige Institution(en) am KIT Fakultät für Informatik (INFORMATIK) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 08.2021 Sprache Englisch Identifikator ISSN: 0001-5903, 1432-0525 KITopen-ID: 1000136121 Erschienen in Acta Informatica Verlag Springer Band 58 Heft 4 Seiten 451-462 Vorab online veröffentlicht am 19.07.2021 Nachgewiesen in DimensionsWeb of ScienceScopus
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