Cycle detection in computation tree logic

We introduce Cycle-CTL⋆, an extension of CTL⋆ with cycle quantifications that are able to predicate over cycles. The introduced logic turns out to be very expressive. Indeed, we prove that it strictly extends CTL⋆ and is orthogonal to μCalculus. We also give an evidence of its usefulness by providing few examples involving non-regular properties. We extensively investigate both the model-checking and satisfiability problems for Cycle-CTL⋆ and some of its variants/fragments.