login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181621 Table by rows, the number E(n;2) of binary-alphabet topological epsilon-machines as a function of the number of states n and edges k. 1
2, 1, 1, 6, 2, 22, 54, 3, 68, 403, 914, 6, 192, 2228, 10886, 21874, 9, 512, 9721, 85974, 360071, 676326, 18, 1312, 37736, 526760, 3809428, 14229762, 25392410 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Table 1, p. 6 of Johnson. 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 epsilon-machines up to seven states and six-letter alphabets.

LINKS

Table of n, a(n) for n=1..29.

B. D. Johnson, J. P. Crutchfield, C. J. Ellison, C. S. McTague, Enumerating Finitary Processes, Oct 30, 2010.

EXAMPLE

n=1, e=1, has 2 epsilon machines; n=1, e=2, has 1 epsilon machine.

n=2, e=2, has 1 epsilon machine; n=2, e=3, has 6 epsilon machines.

n=3, e=3, has 2 epsilon machine; n=3, e=4, has 22 epsilon machines;

n=3, e=5, has 54 epsilon machines.

CROSSREFS

Sequence in context: A085826 A112477 A156984 * A307070 A321615 A084268

Adjacent sequences:  A181618 A181619 A181620 * A181622 A181623 A181624

KEYWORD

nonn,tabf

AUTHOR

Jonathan Vos Post, Nov 01 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 03:49 EST 2021. Contains 349345 sequences. (Running on oeis4.)