Powerset-Theoretic Foundations for HyperAutomata and SuperHyperAutomata

Takaaki  Fujita

doi:10.31181/sa202556

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan. Author

DOI:

https://doi.org/10.31181/sa202556

Keywords:

Hyperstructure, Superhyperstructure, Powerset, HyperAutomata, SuperHyperAutomata

Abstract

Hyperstructure theory, grounded in the powerset construction, offers a rich framework for modeling relationships among elements in a set. Its extension, superhyperstructure, employs the n-th iterated powerset to capture multi-layered hierarchical interactions [1]. A Finite Automaton is a machine with a finite set of states, recognizing regular languages via transitions over input symbols [2, 3, 4]. In this paper, we examine three computational models—classical finite automata, hyperautomata, and superhyperautomata—by providing concise mathematical definitions, illustrative examples, and key properties. Our presentation refines the powerset-based definitions originally given in [5], clarifying how hyperautomata generalize classical automata and how superhyperautomata further generalize hyperautomata. Through this unified treatment, we highlight the expressive hierarchies and closure properties that distinguish these models.

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