# epsilon-machine

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## English[edit]

### Alternative forms[edit]

### Etymology[edit]

*epsilon* + *machine*. Coined by James Crutchfield and Karl Young in their 1989 paper “Inferring Statistical Complexity”.^{[1]}

### Noun[edit]

**epsilon-machine** (*plural* **epsilon-machines**)

- (computational mechanics) A deterministic automaton consisting of a system of causal states and the transitions between them, functioning as the smallest possible maximally predictive model of a stochastic process
**1989**, James Crutchfield and Karl Young, “Inferring Statistical Complexity”:- With a direct measure of an
’s complexity, the theory gives a computation-theoretic foundation to the notions of model optimality and, most importantly, a measure of the computational complexity of estimated models.*ε*-machine

- With a direct measure of an
**2001**, Cosma Rohilla Shalizi, Causal Architecture, Complexity and Self-Organization in Time Series and Cellular Automata:- The
*ϵ*-machine*is*the organization of the process, or at least of the part of it which is relevant to our measurements. It leads to a natural measure of the*statistical complexity*of processes, namely the amount of information needed to specify the state of the. […] Using the*ϵ*-machine, we see that the causal states always form a Markov process. This is satisfying ideologically, and has interesting information-theoretic and ergodic consequences.*ϵ*-machine

**2010**, Sean Harrison Whalen, “Security applications of the epsilon-machine”, abstract:- These predictors, called
**ε-machines**, are a subset of a well known statistical model class called the Hidden Markov Model (HMM). Despite being a subset,**ε-machines**have several important advantages over traditional HMMs. This dissertation illustrates these advantages by applying**ε-machines**to several problems in computer security: anomaly-based intrusion detection in High Performance Computing (HPC) environments, automated protocol reverse engineering, and structural drift.

- These predictors, called
**2011**, Nicolas Brodu, “Reconstruction of epsilon-machines in predictive frameworks and decisional states” in*Advances in Complex Systems*, volume 14, number 05:- This article introduces both a new algorithm for reconstructing
**epsilon-machines**from data, as well as the*decisional states*. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. […] The intrinsic underlying structure of the system is modeled by an**epsilon-machine**and its causal states.

- This article introduces both a new algorithm for reconstructing

### References[edit]

- ^ Shalizi, Cosma Rohilla (2001),
*Causal Architecture, Complexity and Self-Organization in Time Series and Cellular Automata*, page 5