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About this paper
Joe Pratt-Johns, Toby St. Clere Smithe, Chris Guiver, Kevin Hughes, Peter Andras
A categorical framework turns algebraic interaction rules into discrete-time Markov processes over finite multisets of components. The construction recovers Minimal Chemistry Zero, supports multiple protocols, and proves that homomorphisms between algebraic models induce structure-preserving maps between their stochastic dynamics.
Key insights
- The framework separates interaction syntax, algebraic semantics, event protocols, and stochastic population dynamics into independent layers.
- MC0 is recovered by interpreting a binary interaction operation as bounded lambda-term application and combining it with protocols for retaining outputs and deleting molecules.
- Functoriality provides a formal route from detailed algebraic models to coarser stochastic models, while the same construction also covers examples such as number division and communication systems.
Summary by alphaXiv.
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