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A181621
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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