Completeness of Regular Computation

Establish whether every finite functional that uniquely computes a result from finitely many generic probability kernels can be represented using finite combinations of tensor products, left-disintegrations, right-marginalizations, and transpositions, excluding limits and fixed points.

Background

The paper defines regular functionals as finite compositions of tensor products, disintegrations, marginalizations, and transpositions. The authors conjecture that, for generic kernels without additional internal structure such as linearity, these operations exhaust all finite, uniquely defined computations. Establishing this would characterize the computational power of the kernel calculus used throughout the paper and clarify the scope of its completeness claims.