Entropy of trees & tree automata.
Entropy of tree automata = joint spectral radius.
The zero-error coding problem with states.
Approximating zero-error capacities of codes.
Open problems, etc.
Theoretical problem statement
Lift the Shannon/Parry Markov chain of a strongly connected
finite graph to the timed automata settings.
(aka MME of an irreducible SFT)
Practical problem statement
Generate quickly and as uniformly as possible runs of a timed
automaton.
◮ quickly: Step by step simulation as with a finite state Markov
Chain → Stochastic Process Over Runs (SPOR)
◮ ≈ uniformly → SPOR of maximal entropy + asymptotic
equipartition property.