We investigate the complexity of computing entropy of various Markovian models including
Markov Chains (MCs), Interval Markov Chains (IMCs) and Markov Decision Processes (MDPs).
We consider both entropy and entropy rate for general MCs, and study two algorithmic questions,
i.e., entropy approximation problem and entropy threshold problem. The former asks for
an approximation of the entropy/entropy rate within a given precision, whereas the latter aims
to decide whether they exceed a given threshold. We give polynomial-time algorithms for the
approximation problem, and show the threshold problem is in P
CH3 (hence in PSPACE) and
in P assuming some number-theoretic conjectures. Furthermore, we study both questions for
IMCs and MDPs where we aim to maximise the entropy/entropy rate among an infinite family
of MCs associated with the given model. We give various conditional decidability results for
the threshold problem, and show the approximation problem is solvable in polynomial-time via
convex programming