Mere copying processes (partial involutions) are computationally universal

The Geometry of Interaction model shows that simple copying of information between locations suffices for all computation, establishing emergent logic.

Source paper

extracted_from

Information, Processes and Games

Abramsky, Samson

Neighborhood — ranked by edge-count

Findings (1)

finding

Partial involutions form a Linear Combinatory Algebra under function application defined by feedback loops
supports
The set of fixed-point free partial involutions on a countable set, with composition via interaction, yields a linear combinatory algebra, hence a universal model of computation.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

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partial involutionsconcept0.772
Fixed-point free partial injective functions used as simple reversible dynamical processes in Geometry of Interaction.
What are the analogues to Turing-completeness and universality when we are concerned with processes and their behaviours?question0.770
Key open problem: foundational definitions for process models that match the role of Turing completeness for functional computation.
The interactive processes described are reversible in a very strong sense, linking logic and physicsclaim0.759
Partial involutions are invertible; the same structures can axiomatize quantum mechanics and analyse entanglement.
Echoes of similar proportions and angles appear throughout any natural system due to uniform underlying processes, giving a consistent character to different parts.claim0.757