Nondeterministic Behaviours in Double Categorical Systems Theory
Abstract
In this paper, we build double theories capturing the idea of nondeterministic behaviors and trajectories. Following Libkind and Myers' Double Operadic Theory of Systems, we construct monoidal semi double categories of interfaces, along with what we call semimodules of systems, in the case of Moore machines, working with Markov categories with conditionals to handle nondeterminism. We use conditional products in these Markov categories to define trajectories in a compositional way, and represent nondeterministic systems using Markov maps; channels between systems are assumed to be deterministic.
Cite
@article{arxiv.2502.02517,
title = {Nondeterministic Behaviours in Double Categorical Systems Theory},
author = {Paul Zhongpeng Wang},
journal= {arXiv preprint arXiv:2502.02517},
year = {2026}
}
Comments
73 pages; improved the main constructions to allow nondeterministic Markov maps for systems, rewrote the proof for interchange, and removed parametric lenses for simplicity; also corrected a mistake in the definition of y-morphisms