Transition-based vs stated-based acceptance for automata over infinite words

Automata over infinite objects are a well-established model with applications in logic and formal verification. Traditionally, acceptance in such automata is defined based on the set of states visited infinitely often during a run. However, there is a growing trend towards defining acceptance based on transitions rather than states. In this survey, we analyse the reasons for this shift and advocate using transition-based acceptance in the context of automata over infinite words. We present a collection of problems where the choice of formalism has a major impact and discuss the causes of these differences.