Several New Generalized Linear- and Optimum-Time Synchronization Algorithms for Two-Dimensional Rectangular Arrays

• Published in: Lecture notes in computer science pp. 223 - 232
• Main Authors: Umeo, Hiroshi, Hisaoka, Masaya, Teraoka, Masato, Maeda, Masashi
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• ISBN: 3540252614; 9783540252610
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-31834-7_18

We propose several new generalized synchronization algorithms for 2-D cellular arrays. Firstly, a generalized linear-time synchronization algorithm and its 14-state implementation are given. It is shown that there exists a 14-state 2-D CA that can synchronize any m × n rectangular array in m + n + max(r + s , m + n – r – s + 2) – 4 steps with the general at an arbitrary initial position (r, s),where 1 ≤ r ≤ m, 1 ≤ s ≤ n. The generalized linear-time synchronization algorithm is interesting in that it includes an optimum-step synchronization algorithm as a special case where the general is located at one corner. In addition, we propose a noveloptimum-time generalized synchronization scheme that can synchronize any m × n array in m + n + max (m, n) −  min (r, m − r + 1) −  min (s, n − s + 1) − 1 optimum steps.