Characterization of Single Length Cycle Two-Attractor Cellular Automata Using Next-State Rule Minterm Transition Diagram
Suvadip Hazra
Mamata Dalui
Computer Science & Engineering, NIT Durgapur
Durgapur
West Bengal 713209, India
Abstract
Cellular automata (CAs) are simple mathematical models that are effectively being used to analyze and understand the behavior of complex systems. Researchers from a wide range of fields are interested in CAs due to their potential for representing a variety of physical, natural and real-world phenomena. Three-neighborhood one-dimensional CAs, a special class of CAs, have been utilized to develop various applications in the field of very large-scale integration (VLSI) design, error-correcting codes, test pattern generation, cryptography and others. A thorough analysis of a three-neighborhood cellular automaton (CA) with two states per cell is presented in this paper. A graph-based tool called the next-state rule minterm transition diagram (NSRTD) is presented for analyzing the state transition behavior of CAs with fixed points. A linear time mechanism has been proposed for synthesizing a special class of irreversible CAs referred to as single length cycle two-attractor CAs (TACAs), having only two fixed points.
Keywords: cellular automata; TACA; NSRTD
Cite this publication as:
S. Hazra and M. Dalui, “Characterization of Single Length Cycle Two-Attractor Cellular Automata Using Next-State Rule Minterm Transition Diagram,” Complex Systems, 31(4), 2022 pp. 363–388.
https://doi.org/10.25088/ComplexSystems.31.4.363
