Hexagonal Picture Scanning Automata

TL;DR

This paper introduces and analyzes two new classes of finite automata operating on hexagonal grids, extending classical automaton theory to two-dimensional hexagonal structures with specialized traversal patterns.

Contribution

It establishes the theoretical foundations and explores the computational properties and relationships of these novel hexagonal automata models.

Findings

Defined two new classes of hexagonal automata.

Analyzed their computational capabilities and language families.

Explored relationships and equivalences between the models.

Abstract

Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical foundations for these automata models, examines their computational properties, and investigates the relationships and equivalences between the language families they define. The research contributes to the broader understanding of two-dimensional automata theory by extending classical finite automaton concepts to hexagonal geometric structures with specialized traversal patterns.