Automata Theory and Symbolic Dynamics Workshop

We consider the following question: what is the least biased stochastic process over the runs of a given timed automaton? By “least biased”, we mean the one that generates runs with a distribution which is closest to uniform (w.r.t. volume). To answer this question, we first define stochastic processes over runs of timed automata and their entropy, the definition of which is inspired by Shannon’s differential entropy rate. We describe an ergodic stationary stochastic process which maximizes the entropy. Its definition is based on the spectral properties of the operator introduced by Asarin and Degorre, which can be seen as a generalization of adjacency matrices for timed graphs. The maximal entropy stochastic process is defined in an analoguous way to the case of irreducible shifts of finite type. The second main result is an asymptotic equipartition property (AEP) of the runs generated w.r.t. the maximal entropy stochastic process. We finally explain how to achieve a quasi-uniform sampling using this AEP.