FormalCheck Query Language Compared with CTL

The logic CTL can express branching-time attributes that are not expressible with !-automata and conversely the FormalCheck Query Language (FQL) whose semantics is founded on !-automata can express sequentiality and eventuality behaviors that are not expressible with CTL (nor even its extension CTL). Since both CTL and FQL are commonly used in model-checking, it is of interest to compare nonetheless related constructs common to both. In fact, there are subtle but important discrepancies between common FQL expressions and seemingly but not actually equivalent CTL formulae. In some cases these discrepancies illuminate common misunderstandings about the semantical meaning of the given CTL formula, and thus are of interest to CTL users irrespective of FQL. The root cause of these discrepancies is the inability of CTL to express \phase"{ an unbounded succession of disjoint time intervals in which a behavior (i.e., property or constraint) is required to hold. Phase is fundamental to FQL. We show that much of FQL can be expressed by a simple extension CTL + of CTL formed by conjoining \phase bits" to the atomic propositions. However, another behavior fundamental to FQL is strong fairness, which we prove is not expressible even in CTL +. On the other hand, formulae with alternation of path quantiiers fundamental to CTL cannot be expressed in FQL. It is the purpose of this paper to clarify these relationships and distinctions.