Automaton-Based Criteria for Membership in CTL

Computation Tree Logic (CTL) is widely used in formal verification, however, unlike linear temporal logic (LTL), its connection to automata over words and trees is not yet fully understood. Moreover, the long sought connection between LTL and CTL is still missing; It is not known whether their common fragment is decidable, and there are very limited necessary conditions and sufficient conditions for checking whether an LTL formula is definable in CTL.