A Syntactic Approach to Random Walks on Graphs

We use formal language theory to study syntactic behaviour of random walks on graphs. The set of walks, viewed as sets of words, is a recognizable language. As a consequence, a set of random walks can be formally described by a rational fraction or equivalently by an automaton. Applying these techniques, we compute in a unified way various statistical parameters related to random walks, such as mean cover time, and the mean hitting time.

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