Enumerating Finitary Processes

Benjamin D Johnson; James P Crutchfield; Christopher J Ellison; Carl S McTague

doi:10.3390/e26121105

Enumerating Finitary Processes

Entropy (Basel). 2024 Dec 17;26(12):1105. doi: 10.3390/e26121105.

Authors

Benjamin D Johnson^{1

2}, James P Crutchfield^{1

2

3}, Christopher J Ellison^{1

3}, Carl S McTague⁴

Affiliations

¹ Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
² Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
³ Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
⁴ DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK.

Abstract

We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of ϵ-machines. We characterize ϵ-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large class down to that of ϵ-machines. As an application, we exactly enumerate topological ϵ-machines up to eight states and six-letter alphabets.

Keywords: epsilon-machine; orderly enumeration.

Abstract

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