CTLIs Complete for Double Exponential Time

Jan Johannsen, Martin Lange

Abstract: We show that the satisfiability problem for CTL+, the branching time logic that allows boolean combinations of path formulas inside a path quantifier but no nesting of them, is 2-EXPTIME-hard. The construction is inspired by Vardi and Stockmeyer’s 2-EXPTIME-hardness proof of CTL*’s satisfiability problem. As a consequence, there is no subexponential reduction from CTL+ to CTL which preserves satisfiability.