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When I have a simple markov chain with a fixed number of states and a fixed number of terminal states, does weighting transitions from a training set of longer sequences cause the chain to produce longer output when starting in initial state and following to a terminal state?

Real world example: A markov chain is created from a text corpus by a simple transition funktion $t(w_1)=w_2, t: W\to W$ with one special state $w_0$ for the start of a sentence and a set $S \subset W$ of terminal states, i.e. words which were at the end of a sentence.

Will a markov chain create longer sequences on average?

I am not sure, but it seems like it does not neccessarily have to, e.g. when the distributions of terminal states for a word and of non-terminal states for a word are similar.

allo
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  • As a hint: why would it generate longer output on average? Try constructing an example of a markov chain which would definitely generate a shorter length sentence by having a very high chance of going to a terminal state. – Jan Oct 09 '18 at 16:16
  • Train with ABBB...BBBA as corpus and 50% of generated output will be A – Hagen von Eitzen Oct 09 '18 at 16:21
  • Pro longer: Add a long sentence with unique words and the chain will reproduce it. Pro "does not matter": Add more sentences with common words and the chain can take shortcuts to words near terminal states. Pro shorter: Sentences may contain a common second / second last word, which will produce a very short shortcut. I do not see to which behavior longer/shorter sentences will converge. Are there theorems proving things related to this? – allo Oct 09 '18 at 21:26

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