Construction Theory, Self-Replication, and the Halting Problem
  This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that self-replication of von Neumann's universal constructors holds a close similarity to circular computational processes of universal computers that appear in Turing's original proof of the undecidability of the halting problem. The result indicates the possibility of reinterpreting a self-replicating biological organism as embodying an attempt to solve the halting problem for a {\em diagonal} input in the context of construction. This attempt will never be completed because of the indefinite cascade of self-computation/construction, which accounts for the undecidability of the halting problem and also agrees well with the fact that life has maintained its reproductive activity for an indefinitely long period of time. 
Hiroki Sayama