Probabilistic models for pattern statistics
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.
pattern statistics markov chains probabilistic automata rational formal series