Coinductive Models of Finite Computing Agents

This paper explores the role of coinductive methods in modeling finite interactive computing agents. The computational extension of computing agents from algorithms to interaction parallels the mathematical extension of set theory and algebra from inductive to coinductive models. Maximal fixed points are shown to play a role in models of observation that parallels minimal fixed points in inductive mathematics. The impact of interactive (coinductive) models on Church’s thesis and the connection between incompleteness and greater expressiveness are examined. A final section shows that actual software systems are interactive rather than algorithmic. Coinductive models could become as important as inductive models for software technology as computer applications become increasingly interactive.