Simulation Models: The Combinatory Automaton

Piero Mella
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Piero Mella: University of Pavia

Chapter Chapter 3 in The Combinatory Systems Theory, 2025, pp 221-314 from Springer

Abstract: Abstract The chapter introduces the concept of Combinatory Automaton, a tool for simulating, mainly in probabilistic terms, the different classes of combinatory systems. Combinatory Automata models offer a simulation of the dynamics of combinatory systems 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 th depends on a synthetic global variable whose values derive from some “combination” operation carried out on the values of the cells in successive iterations; the synthetic global variable represents the synthetic state of the automaton. The micro-macro feedback operating in successive moments for a certain period connects the analytical values of the cells and the synthetic state of the automaton. This chapter seeks 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.

Keywords: Stochastic Combinatory Automaton; Boolean automaton; Reversible and irreversible Combinatory Automaton; Fields of probabilities; Oscillating macro behavior; “Chaotic” macro behavior (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:prochp:978-3-031-86946-4_3

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DOI: 10.1007/978-3-031-86946-4_3

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