A181554 The number E_{n,2} of n-state topological epsilon-machines over a binary alphabet.

3, 7, 78, 1388, 35186, 1132613, 43997426, 1993473480

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.

S. Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), p. 957.

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: A108537 A364660 A219292 * A116294 A077793 A175236

Adjacent sequences: A181551 A181552 A181553 * A181555 A181556 A181557

Keyword

hard,nonn

Author

James P. Crutchfield, Oct 30 2010

Extensions

a(8) from James P. Crutchfield, Nov 22 2010

Status

approved