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 Cellular automata (CAs) are simple mathematical models that are effectively being used to analyze and understand the behavior of com- plex 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 applica- tions 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 Introduction 1. Cellular automata (CAs), a significant development in the history of computing, were first developed by John von Neumann in the 1950s to study self-reproducing automata [1]. Wolfram established that CAs could be used to describe complex natural events and subsequently set the foundation for a theory of CAs, which are defined as discrete dynamic systems in which local interactions among components cause global changes in space and time [2]. Due to the simple but sophisti- cated structure, three-neighborhood two-state CAs have recently proved to be an effective modeling tool [3–10]. Characterizing such a machine, on the other hand, is still under study. While analyzing the state space of a three-neighborhood cellular automaton (CA), the https://doi.org/10.25088/ComplexSystems.31.4.363