A Class of Minimum-Time Minimum-State-Change Generalized FSSP Algorithms

• Published in: Cellular Automata Vol. 9863; pp. 144 - 154
• Main Authors: Umeo, Hiroshi, Imai, Keisuke
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2016; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Cellular Automaton; Cellular Space; Initial General; Internal State; Quiescent State; User interface design & usability
• ISBN: 9783319443645; 331944364X
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-44365-2_14

The firing squad synchronization problem (FSSP, for short) on cellular automata has been studied extensively for more than fifty years, and a rich variety of FSSP algorithms has been proposed. Here we consider the FSSP from a view point of state-change-complexity that models the energy consumption of SRAM-type storage with which cellular automata might be built. In the present paper, we propose a class of minimum-time, minimum-state-change generalized FSSP (GFSSP, for short) algorithms for synchronizing any one-dimensional (1D) cellular automaton, where the synchronization operations are started from any cell in the array. We construct two minimum-time minimum-state-change GFSSP algorithms: one is based on Goto’s algorithm, known as the first minimum-time FSSP algorithm that is reconstructed again recently in Umeo et al. [13], and the other is based on Gerken’s one. These algorithms are optimum not only in time but also in state-change complexity.