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Graded CTL* over Finite Paths

In this paper we introduce Graded Computation Tree Logic over finite paths (GCTLf , for short), a variant of Computation Tree Logic CTL∗, in which path quantifiers are interpreted over finite paths and can count the number of such paths. State formulas of GCTLf are interpreted over Kripke structures with a designated set of states, which we call "check points". These special states serve to delineate the end points of the finite executions. The syntax of GCTLf has path quantifiers of the form E≥gψ which express that there are at least g many distinct finite paths that a) end in a check point, and b) satisfy ψ. After defining and justifying the logic GCTLf , we solve its model checking problem and establish that its computational complexity is PSPACE-complete.