Model-checking graded computation-tree logic with finite path semantics

Abstract

This paper introduces Graded Computation Tree Logic with finite path semantics (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. 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 satisfy ψ. After defining and justifying the logic GCTLf⁎, we solve its model checking problem and establish that its computational complexity is PSPACE-complete. Moreover, we investigate GCTLf⁎ under the imperfect information setting. Precisely, we introduce GCTLKf⁎, an epistemic extension of GCTLf⁎ and prove that the model checking problem also in this case is PSPACE-complete.