On the Hybrid Extension of CTL and CTL+

The paper studies the expressivity, relative succinctness and complexity of satisfiability for hybrid extensions of the branching-time logics CTL and CTL by variables. Previous complexity results show that only fragments with one variable do have elementary complexity. It is shown that HCTL and HCTL, the hybrid extensions with one variable of CTL and CTL, respectively, are expressively equivalent but HCTL is exponentially more succinct than HCTL. On the other hand, HCTL, the hybrid extension of CTL with arbitrarily many variables does not capture CTL, as it even cannot express the simple CTL property EGFp. The satisfiability problem for HCTL is complete for triply exponential time, this remains true for quite weak fragments and quite strong extensions of the logic.