  In this paper, we show how a construction of an implicit complexity model can
be implemented using concepts coming from the core of von Neumann algebras.
Namely, our aim is to gain an understanding of classical computation in terms
of the hyperfinite $\mathrm{II}_1$ factor, starting from the class of Kalmar
recursive functions. More methodologically, we address the problem of finding
the right perspective from which to view the new relation between computation
and combinatorial aspects in operator algebras. The rich structure of discrete
invariants may provide a mathematical setting able to shed light on some basic
combinatorial phenomena that are at the basis of our understanding of
complexity.
