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In this work we study some probabilistic models for the random generation of words over a given alphabet
used in the literature in connection with pattern statistics.
Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given position
only depends on a finite number of previous occurrences) and the stochastic models that
can generate a word of given length from a regular language under uniform distribution.
We present some results that show the differences between these two stochastic models and their
relationship with the rational probabilistic measures.
We prove that a word of length n from a finitely
ambiguous context-free language can be generated at random under
uniform distribution in O(n2 log n) time by a probabilistic random access machine assuming a logarithmic cost criterion.
We also show that the same problem can be solved in polynomial
time for every language accepted by a polynomial time 1-NAuxPDA
with polynomially bounded ambiguity.
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