Autopoietic automata: Complexity issues in offspring-producing evolving processes

We introduce a new formal computational model designed for studying the information transfer among the generations of offspring-producing evolving machines — so-called autopoietic automata. These can be seen as nondeterministic finite state transducers whose “program” can become a subject of their own processing. An autopoietic automaton can algorithmically generate an offspring controlled by a program which is a modification of its parent’s program. Autopoietic automata offer a neat framework for investigating computational and complexity issues in the evolutionary self-reproducing processes. We show that the computational power of lineages of autopoietic automata is equal to that of an interactive nondeterministic Turing machine. We also prove that there exists an autopoietic automaton giving rise to an unlimited evolution, provided that suitable inputs are delivered to individual automata. However, the problem of sustainable evolution, asking whether for an arbitrary autopoietic automaton and arbitrary inputs there is an infinite lineage of its offspring, is undecidable.