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A Tangled Hierarchy of Graph-Constructing Graphs

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5 Author(s)

The traditional construction paradigm of machine and tape is reformulated in a functionally homogeneous space of directed graph structures. Hierarchy-based roles, normally appointed to actors in a construction process, are dissolved and replaced by symmetric, level-less engagement. The separation between static (information carrying) and active (information processing) structures, imposed by mandate of the rules or physics in earlier theoretical models, results instead purely firom graph topology. While encompassing traditional machine-tape paradigms as a special case, the formalism is shown to incorporate a wider class of construction relations. Exploiting its flexibility, a representation of a Turing machine is demonstrated, establishing computation universality. The concept of a “Tangled Construction Hierarchy” is introduced.