  Kolmogorov's representation theorem provides a framework for decomposing any
arbitrary real-valued, multivariate, and continuous function into a two-layer
nested superposition of a finite number of functions. The functions at these
two layers, are referred to as the inner and outer functions with the key
property that the design of the inner functions is independent of that of the
original function of interest to be computed. This brings modularity and
universality to the design of the inner function, and subsequently, a part of
computation. This paper capitalizes on such modularity and universality in
functional representation to propose two frameworks for distributed computation
over the additive multiple access channels (MACs). In the first framework, each
source encodes the inner representations and sends them over the additive MAC.
Subsequently, the receiver computes the outer functions to compute the function
of interest. Transmitting the values of the inner functions instead of the
messages directly leads to compression gains. In the second approach, in order
to further increase the compression rate, the framework aims to also bring
computing the outer functions to the source sites. Specifically, each source
employs a graph-coloring-based approach to perform joint functional compression
of the inner and the outer functions, which may attain further compression
savings over the former. These modular encoding schemes provide an exact
representation in the asymptotic regime and the non-asymptotic regime.
Contrasting these with the baseline model where sources directly transmit data
over MAC, we observe gains. To showcase the gains of these two frameworks and
their discrepancies, they are applied to a number of commonly used computations
in distributed systems, e.g., computing products, $\ell_m$-norms, polynomial
functions, extremum values of functions, and affine transformations.
