Volume 35, Issue 2 (2026)

Characterization of Maximal Length Cellular Automata
Using NSRTD

Som Banerjee
Mamata Dalui
Department of Computer Science and Engineering
National Institute of Technology, Durgapur
West Bengal 713209, India

Abstract

Maximal length cellular automata (CAs) have gained significant attention from researchers due to their applications in different areas like random number generation, cryptography and test pattern generation. This paper reports the theoretical framework of the next state rule min term transition diagram (NSRTD) for the characterization of maximal length CAs in null-boundary condition. The proposed solution helps in verifying whether a given cellular automaton (CA) is a maximal length CA or not in $O\left(2^n\right)$ time. Also, the proposed solution can identify and eliminate a CA candidate that fails to configure a maximal length CA in linear time.

Keywords: cellular automata; maximal length CA; fixed-point attractor; NSRTD; null boundary CA

Cite this publication as:
S. Banerjee and M. Dalui, “Characterization of Maximal Length Cellular Automata Using NSRTD,” Complex Systems, 35(2), 2026 pp. 141–160.
https://doi.org/10.25088/ComplexSystems.35.2.141