Simulation Models. The Combinatory Automaton

Abstract

Combinatory Automata models offer a description of the behavior of combinatory systems and simulate their dynamics in terms of the dynamics, expressed in probability terms, of the state of the system and the state of the individual elements. A Combinatory Automaton is composed of a matrix, each of whose cells contains a variable representing the state of an agent. The value of each cell at time t_h depends on a synthetic global variable whose values derive from some operation carried out on the values of the cells; the synthetic global variable represents the synthetic state of the automaton. The micro-macro feedback connects the analytical values of the cells and the synthetic state of the automaton. This Chapter try to demonstrate, through simple examples, that combinatory systems represent a wide range of behaviors of collectivities and that Combinatory Automata are a powerful tool for simulating the most relevant combinatory systems.