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A181554 The number E_{n,2} of n-state topological epsilon-machines over a binary alphabet. 0
3, 7, 78, 1388, 35186, 1132613, 43997426, 1993473480 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Topological epsilon-machines are a class of minimal, deterministic finite automata with a single recurrent component all of whose states are start and final states. These, in turn, can be represented as a class of labeled directed graphs that are strongly connected. They also represent the skeletons of finite-memory stochastic processes or sofic subshifts.

Row sums of A181621. - Jonathan Vos Post, Nov 03 2010

LINKS

Table of n, a(n) for n=1..8.

B. D. Johnson, J. P. Crutchfield, C. J. Ellison and C. S. McTague, Enumerating Finitary Processes arXiv:1011.0036 [cs.FL],  2010-2012.

FORMULA

a(n) = Sum_{e=1..(n+1)} A181621(e,i} = Sum_{k=1..(n+1)} E(n;2) of binary-alphabet topological epsilon-machines with n states and k edges. - Jonathan Vos Post, Nov 03 2010

CROSSREFS

Cf. A181621.

Sequence in context: A103737 A108537 A219292 * A116294 A077793 A175236

Adjacent sequences:  A181551 A181552 A181553 * A181555 A181556 A181557

KEYWORD

hard,nonn

AUTHOR

James P. Crutchfield, Oct 30 2010

EXTENSIONS

More terms added from recent calculations

STATUS

approved

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Last modified October 27 13:19 EDT 2021. Contains 348276 sequences. (Running on oeis4.)