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This should be fairly standard, but I fail to google it, and nothing on the matter is on Math.SE.

How do we call the opposite of an absorbing state? If we think about Markov chains/systems, that would be a state such that there is no positive transition probability to that state from any other one.

In other words, a state that - if we didn't start in it - we would never end up in it.

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  • $\begingroup$ I don't think there is a standard term for such a thing, but a word that is used in similar contexts (usually as opposed to "attractive") is "repelling" $\endgroup$ Feb 6, 2015 at 17:15
  • $\begingroup$ In terms of flow diagrams, absorbing states are called "sinks" and the state you describe are called "sources". $\endgroup$
    – JMoravitz
    Feb 6, 2015 at 17:23

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In the context of finite state automata, such states are called Garden of Eden states.

E.F. Moore proved existence of such states of certain infinite automata in Machine models of self-reproduction, Proc. Sympos. Appl. Math., Vol. 14, pp. 17-34 (1963). See Amorosa and Cooper (1970) for some extensions to finite configurations.

Moore attributed the name to John Tukey in the 1950's.

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