ABSTRACT
A novel class of models for functional integration and transformation in biological, neural, and social sciences based on random grammars is proposed. A major question is the relation between grammars and Boolean world transition matrices. This chapter considers alternative approaches to generate in some ordered way the set of "all possible" mappings of strings into strings. It describes the extensions by Walter Font ana concerning autocatalytic sets are exciting and important. All point towards a new way to investigate the emergence of functional integration and adaptation in complex systems. The chapter suggests an economic context where strings are goods that such formal undecidability may map into the logical requirement for bounded rationality in economic agents, and an equal logical requirement for incomplete markets. It uses such unique numberings to produce a deterministic mapping from the state of the "world" to the next state. The chapter also considers the denumerably ordered power set of symbol strings whose lengths may be arbitrary.
