• Corpus ID: 481764

# Enumerating Finitary Processes

@article{Johnson2010EnumeratingFP,
title={Enumerating Finitary Processes},
author={B. D. Johnson and James P. Crutchfield and Christopher J. Ellison and Carl S. McTague},
journal={ArXiv},
year={2010},
volume={abs/1011.0036}
}
Author(s): Johnson, B. D.; Crutchfield, J. P.; Ellison, C. J.; McTague, C. S. | Abstract: We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-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 epsilon-machines. As an application, we exactly enumerate topological…
18 Citations

## Figures, Tables, and Topics from this paper

Many Roads to Synchrony: Natural Time Scales and Their Algorithms
• Mathematics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
It is demonstrated that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes by drawing out the roles played in statistical mechanical spin systems by these two complementary length scales.
Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited
• Computer Science, Physics
ArXiv
• 2019
There is an important and underappreciated role for methods that infer "causal states" or "predictive state representations" in generalized linear models, RCs and RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA).
Study of Time Reversal in Complex Systems
Abstract : In this paper we present conclusions of a study of irreversibility in physical processes, using the conceptual formalism of the epsilon-machine. The causal irreversibility is examined, in
Information Symmetries in Irreversible Processes
• Mathematics, Physics
Chaos
• 2011
This work examines stationary processes represented or generated by edge-emitting, finite-state hidden Markov models, and shows how to directly calculate a process's fundamental information properties, many of which are otherwise only poorly approximated via process samples.
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s) and shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.
Measures and Metrics of Information Processing in Complex Systems: A Rope of Sand.
A mathematical framework is established where natural systems are represented by a canonical form of edge-labeled hidden Markov models called-machines and a semantic understanding of information generation emerges, labeling some information generation as ephemeral, having no lasting eeects on the system, and the rest as bound, playing a role temporal structure.
Computational Mechanics of Input–Output Processes: Structured Transformations and the $$\epsilon$$ϵ-Transducer
• Mathematics, Physics
• 2014
This work lays the foundation of a structural analysis of mechanisms that support information flow between processes, treating joint processes and processes with input and obtaining an analogous optimal model of the stochastic mapping between them.
Occam’s Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel
• Computer Science, Medicine
Scientific reports
• 2016
It is demonstrated that maximum compression is determined by the process’ cryptic order–a classical, topological property closely allied to Markov order, itself a measure of historical dependence.
Finitary Process Evolution I: Information Geometry of Configuration Space and the Process-Replicator Dynamics
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic
Structure and Randomness of Continuous-Time, Discrete-Event Processes
• Computer Science, Physics
ArXiv
• 2017
The entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes—are calculated for the first time.

## References

SHOWING 1-10 OF 30 REFERENCES
Enumeration and Generation of Initially Connected Deterministic Finite Automata
The representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we present a (unique) string representation for (complete) initially-connected
Enumeration and random generation of accessible automata
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2007
We present a bijection between the set A"n of deterministic and accessible automata with n states on a k-letters alphabet and some diagrams, which can themselves be represented as partitions of a set
Enumeration and generation with a string automata representation
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2006
This work shows how a (unique) string representation for (complete) initially-connected deterministic automata (ICDFAs) with n states over an alphabet of k symbols can be used for counting, exact enumeration, sampling and optimal coding, not only the set of ICDFAs but, to some extent, theSet of regular languages.
Automated pattern detection - An algorithm for constructing optimally synchronizing multi-regular language filters
• Computer Science, Physics
Theor. Comput. Sci.
• 2006
A finite transducer is presented that requires only a finite amount of memory, runs in linear time, and gives immediate output for each letter read; it is, moreover, the best possible finite-state approximation with these three features.
An Introduction to Automata Theory
Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial
Random generation of DFAs
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2005
This document gives a generalization on the alphabet size of the method that is described in Nicaud's thesis for randomly generating complete DFAs, and provides experimental results that show that most of the accessible completeDFAs built on an alphabet of size greater than 2 are minimal.
Introduction to Automata Theory, Languages and Computation
• Computer Science
• 1979
This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Principle of Inclusion-Exclusion on Semilattices
• H. Narushima
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 1974
An enumeration theorem under lattice action is introduced and two applications of the theorem are described to a Boolean lattice of sets and a partition lattICE of a set.
On the Number of Distinct Languages Accepted by Finite Automata with n States
• Mathematics, Computer Science
DCFS
• 2001
We give asymptotic estimates and some explicit computations for both the number of distinct languages and the number of distinct finite languages over a k-letter alphabet that are accepted by
Denumerable Markov chains
• Mathematics
• 1969
This textbook provides a systematic treatment of denumerable Markov chains, covering both the foundations of the subject and topics in potential theory and boundary theory. It is a discussion of