Model Checking: AP deterministic

What is action deterministic and AP-deterministic in model checking?

[write about]

A model – what is a model? From where did it come from?

– what is the formal definition of a model? – what is model theory?

– how is logic connected to this? – how are finite automate connected to this?

– what is action-deterministic? – what is AP-deterministic and why do we need it?